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RES 342 Final Exam An independent consumer testing lab preformed a statistical test on 25 type-C alkaline batteries and calculated the mean life for a particular use before they failed was 22.5 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.1 hours. Information on the package states that the batteries should last 24 hours. The test question was if this difference between the test statistics and the stated life of the battery was significant? The .05 significant level was selected for the test. Which is the correct statement? What is the critical value for a two-tail, one sample hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 23? The area of rejection, on a bell shaped curve, defines the location of all those values that are K & S Construction, located in Phoenix, Arizona, is working on its business plan for the upcoming year. They did a study to determine if they should focus on building condominiums or individual houses. A building study, which had been conducted by the state, indicated that 60 percent of those families looking to buy a home in Arizona desired to buy a condominium. K & S Construction wanted to know if this figure applied to Phoenix. They collected a sample of 500 individuals that had expressed plans to buy a new home. The z-distribution was selected for this proportion test. The null hypothesis is p = 0.60 and the alternate is p ? 0.60. The significant level selected was .05. From the sample of 500, it was determined that 290 wanted to buy a condominium. What decision should be made regarding the null hypothesis? Doi Winery has two wine shops in the neighboring towns of Seamen and Batavia. The favorite wine, as advertised, is Raspberry wine. A survey of 300 customers at the Seamen store revealed that 225 individuals preferred the Raspberry wine while 290 out of 400 in Batavia preferred the same flavor. To test the hypothesis that there was no difference in preferences in the two towns, what is the alternate hypothesis? A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test she wished to perform might have unacceptable large possibilities of Type II error, ß. Which of the following would solve this problem? When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are Thomas Delivery has a fleet of 24 trucks that are utilized for the companies; business. Electro-Lite, a manufacturer of spark plugs, claims that its spark plugs have an average life in excess of 25,000 miles. The purchasing agent at Thomas Delivery purchased 24 sets and found that the sample average life was 26,300 miles, the sample standard deviation was 1,500 miles, and the computed test statistic was t = 3.423. Based on these findings, at the 0.05 level, is there enough evidence to accept the manufacturer's claim? If the paired differences are normal in a test of mean differences, then the distribution used for testing is the Flash Jolt, a manufacturer of camera equipment, annually introduces new models in the fall of the year. At the conclusion of the Christmas season, retail dealers are contacted regarding their stock on hand of each piece of equipment. It has been discovered that unless 47% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. At the end of the 2009 Christmas shopping season a survey of 100 dealers indicated that 45% of Flash Jolt equipment had been sold. It was decided to continue production levels at the current levels. The statistical test was conducted at the 0.05 level. Computed z = 0.40. Newtons, a tire manufacturer, wanted to set a mileage guarantee on its new Road Warrior 60 tire. A sample test of 500 tires revealed that the tires mileage is normally distributed with a mean of 50,000 miles and a standard deviation of 1,750 miles. The warranty on the tires is presently set at 47,500 miles. The z-test statistic result was 1.43. The manufacturer wanted to determine if the tires were exceeding the guarantee. At the .05 significant level, it was concluded that the tires are exceeding the manufacturers guarantee. In a test for the equality of two variances (two-tailed), when the populations are normal, a 5% level of significance was used. Sample sizes were n1 = 13 and n2 = 10. The upper critical value for the test is Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? PRODUCT FIFO (F) LIFO (L) 1 225 221 2 119 100 3 100 113 4 212 200 5 248 245 The 5% level of significance was selected for the t value. This example is what type of test? The owner of a bottling company is considering buying a new bottling machine. He has been testing two different machines that are being considered. After collecting 300 samples from each machine over several weeks, he was able to conduct a two sample z test.

He decided to utilize a 0.05 significant level for the test. The test was to address the claim that the mean weight of the bottles filled by the Orno machine was greater than the mean weight of the bottles filled by the Edne machine. The test statistics was 2.21. What is the decision regarding the hypothesis? When is it appropriate to use the paired difference t-test? You are conducting a two-tailed test of means, but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are A consumer researcher is testing the difference between two proportions at the 0.05 level of significance. The researcher was utilizing the z distribution for the test. If the computed test statistic z value was 1.12, what was the decision? Watsons TV claims that their televisions have the best performance record on the market. They advertise that after 3 years only 10% of their sold televisions have had any type of repairs. The president of the company wanted to confirm that this statement was correct. To do this, a sample of 60 sets was taken of sets that had been sold and were at least 3 years old. Twelve percent of these television sets had been in for repair. The null hypothesis is that there is no difference between the stated percent and the sample data. At the .05 significant level, what can we conclude about the null hypothesis? New college business graduates are finding it difficult to get a job. A business journal has reported that only one in five graduates is able to find a job within 6 months of their graduation. A report by the University of Phoenix indicated that out of a survey of 300 recent business graduates, 75 had jobs. You are a business major at the University of Phoenix and have a concern about getting a job. Based on this data, will a graduate of the University of Phoenix have a better chance of getting a job in the first 6 months after graduation? Use the .05 significant level for the test. A trolley system is being planned for the downtown area of Cincinnati, Ohio. To be able to proceed with this project, planners have indicated that at least 20% of the residents of the areas that would be covered need to support the idea. To determine the feelings of these city residents, a sample of 300 residents was taken. Seventeen percent of the sample responded that they would ride the trolley. Is this enough evidence for the project to proceed? Use the .05 level of significant. Mr. Thomas owns three different restaurants in Cincinnati, Ohio. He is concerned about the profitability of the restaurants. There are monthly differences between the restaurants and he wants to determine if the differences in profit are significant. Mr. Thomas wants to do a statistical test to see if he should be concerned. The best test to address this problem would be Analysis of variance is used to In the metro area there are four major supermarket chains. To determine if there was a difference between these stores, regarding their pricing of food, a consumer group did a test. In the Eastgate area of town, each of the supermarket chains has a store. Twenty-five common household items were selected for the test. These items were purchased at each of the four stores and the prices were compared. To analyze this data, what would be the best statistical test to use? Robinson, a large department store, wanted to example to look at which credit cards were being utilized for purchases. A sample of 18 credit card sales was taken and recorded. The amounts charged for each of three different credit cards, MasterCard, Visa, and Discover, were: six MasterCard sales, seven Visa sales, and five Discover sales. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic? In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? What are the assumptions required for nonparametric tests regarding the shape of the population distribution? The chi-square distribution becomes more symmetrical as Of the values for a chi-squared test statistic listed below, which one is most likely to lead to rejecting the null hypothesis in a goodness-of-fit test? The nonparametric counterpart of the randomized block model of the ANOVA is the The city of Denver has several golf courses around the city. The Recreational Park manager is trying to set the schedule for the employees at these courses. His concern is that he wants to have enough staff to handle the daily demands but to not be overstaffed. He has concerns about the next years budget and is trying to curb expenses where possible. To be able to make a decision regarding staffing, he collected data regarding the number of rounds of golf played during the week. The weekend was excluded because the weekends are always very busy. He wanted to see if there was a significant difference between the days of the week in terms of rounds being played. If there was a difference, then he could use this information to help make staffing decisions. The result of the data collection is as follows: Day of Week Rounds Monday 150 Tuesday 90 Wednesday 120 Thursday 100 Friday 140 What is the result of the statistical test? Can the managers staff schedule vary for different days of the week? Use the chi square distribution at the .05 significant level What is your decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 7.815 and the computed value is 6.789? Clermont Savings and Loan has four branches located throughout the county. The activity level at these four branches appears to be different but the manger needs verification. Turnover rate, how quickly money is withdrawn from an account after being deposited, was selected as the variable to be measured. A total sample of 22 accounts was collected from the four Branches. The Kruskal-Wallis test, at the .01 significant level, was selected for the statistical analysis. The null hypothesis being tested was that the population distribution between the four branches is identical. The test statistics was H = 12.453. What is the correct interpretation of this result? The Big Toy House is a local company that specializes in selling children outdoor playhouses. With many businesses there is a certain amount of difficulty in collecting money on past due accounts. This has become a concern of the owner. A recent trade magazine indicated that the national averages for account receivable were: 65% current, 25% late, and 10% not collectable. A recent study of the companys records indicated that 60 percent of the account receivable is current. Thirty percent of the accounts were late and the remaining 10% of receivable were viewed as being not collectable. To determine if his store was in-line with the national average, the manager had a statistical analysis performed. The chi square test was selected for the analysis and the .05 significant level was used. The test statistics was X² = 6.725. What is the correct decision regarding this result? What is the range of values for a coefficient of correlation? The Ohio Electric Company is investigating electric consumption by single family homes based on the number of rooms. The investigators wanted to determine the relationship between number of rooms and electric consumption in kilowatt-hours (thousands). A sample of 12 homes was selected and the data is as follows: Number of Rooms Kilowatt-Hours Number of Rooms Kilowatt-Hours 10 10 8 9 9 8 10 11 7 6 10 9 12 13 8 9 8 7 6 7 11 12 5 6 What percent of the variation is explained by the variable, number of rooms? The Golden Park and Recreation Department wants to determine a better way to estimate income at the various recreational centers. One relationship that was investigated was between family size and amount spent on recreation. The question was if smaller families spent less money than larger families. A regression analysis tool was selected to be used to address this question. Data was collected from 15 member families regarding what they spent each week on recreation. Their data was as follows: Family Size Amount Spent Family Size Amount Spent Family Size Amount Spent 4 $109 3 $101 3 $115 5 114 4 120 6 174 3 161 4 125 5 156 5 159 6 170 4 145 5 164 3 104 5 145 Compute the coefficient of correlation When an insurance company is going to write a new home owner policy, one concern is the distance between the house and the nearest fire department station. This is one factor that goes in to determining the cost of the insurance for the home owner. ETB Insurance Company wants to determine if there is a relationship between the distance to a fire station and the amount of fire damage to a house. A random sample of 50 claims was selected for analysis. The correlation coefficient was 0.78. Which is the correct interpretation and recommendation? The Actuarial Department of an insurance company was assigned the task of determining the relationship between the distance to a fire station and the amount of damage to a house. This is one factor that is utilized in determining the cost of insurance for a home owner. A sample of 35 claims was selected from last year. When the analysis was completed the following regression equation was the result. (X is the distance to a fire station and Y' is the amount of damage in thousands of dollars) Y' = 11.65 + 5.12X If a house was 10 miles from the fire station, what would be the best estimate of the cost of damages to the house? In the least squares equation, Y' = 12 + 25X the value of 25 indicates If the net regression coefficients in the population are significantly different from zero, what can be concluded? If there are four independent variables in a multiple regression equation, there are also four Which of the following statements about multiple regression is TRUE? Given the trend equation Y' = 24 + 0.6t (base year = 2006), what would be the forecast value for 2010? If a quarterly seasonal index is 0.66, it implies that If the least squares equation for Marys Clothing sales data from 2004 to 2008 is represented by the equation Y' = 12 + 1.1t (in $ millions). What is the value of t and the forecast for 2010? Big House Lumber Company, located in Dayton, Ohio, is preparing its annual business report. The manager has performed an analysis of the business annual sales starting in 2004 and concluding with 2009. This analysis produced an annual sales linear trend equation of Y' = 10.0989 + 0.14213t. The manager has been indicating to the companys investors that sales in 2011 will exceed $11.5 million dollars. Is the manager statement accurate? Midwest State University Office of Registrar is reviewing the universitys enrollment for the past 10 years. It is know that there are seasonal variable that affects the universitys enrollment. To be better able to address business decisions that are affected by enrollment, an analysis of data was necessary. The school operates on a quarter system of enrollment starting typically with fall quarter and ending with summer quarter. The analysis of the data produced these four quarterly indexes. Fal Winter Spring Summer 1.2617 1.1896 1.040 0.4447 Which statement is correct based on this analysis? The owner of a local construction company that specializes in outdoor structures desires to make a prediction regarding the next business year sales. Expansion of the business is one possible decision that could be made. It has been determined that the business needs to be at least $8 million dollars in annual sales before expansion could be considered. The following is data for the past 6 years. (Sales in millions of dollars.) Year Sales Year Sales 2004 7.45 2007 7.94 2005 7.83 2008 7.76 2006 8.07 2009 7.90 The statistical analysis of the data produced this least square trend equation. Y' = 7.634 + 0.05457t What should the owner's decision be regarding expansion in 2010? The area of rejection, on a bell shaped curve, defines the location of all those values that are If the decision is to reject the null hypothesis of no difference between two population parameters, z distribution at the .01 significant level, what is the correct statement of the alternate hypothesis and rejection region? The statement that determines if the null hypothesis is rejected or not is called the The Roman Senate has become concerned about the loyalty of the army in Gaul commanded by Julius Caesar. They claim that, of the 80,000 men in the army, at least 28,000 are foreign barbarians. Caesar believes there are fewer barbarians, so the Senate should not worry. He polls one legion of 1,000 men and finds that 340 of them are barbarians. What is the test statistic for this hypothesis test? A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test she wished to perform might have unacceptable large possibilities of Type II error, ß. Which of the following would solve this problem? In classical hypothesis testing, the test statistic is to the critical value what the ________________. When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are If the paired differences are normal in a test of mean differences, then the distribution used for testing is the You are conducting a two-tailed test of means but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is One hundred women were polled and 60 reported successfully communicating an automobile problem to an auto repairman. A sample of 150 men had 95 reporting the same success. The value of the test statistic for a test of the equality of proportions is A recent study by College Stat Company reported a nationwide survey of college students determined that students spend 2 hours studying for each hour in the classroom. Professor Baker at State College wants to determine whether the time students spend at her college is significantly different from the national average of 2 hours. A random sample of 20 statistics students resulted in an average of 1.75 hours with a standard deviation of 0.24 hours. A t-test was conducted at the 5% level of significance. The calculated value of t was -4.03. What was Professor Baker decision? Newtons, a tire manufacturer, wanted to set a mileage guarantee on its new Road Warrior 60 tire. A sample test of 500 tires revealed that the tires mileage is normally distributed with a mean of 50,000 miles and a standard deviation of 1,750 miles. The warranty on the tires is presently set at 47,500 miles. The z-test statistic result was 1.43. The manufacturer wanted to determine if the tires were exceeding the guarantee. At the .05 significant level, it was concluded that the tires are exceeding the manufacturers guarantee. Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? Product FIFO (F) LIFO (L) 1 225 221 2 119 100 3 100 113 4 212 200 5 248 245 The 5% level of significance was selected for the t value. This example is what type of test? When is it appropriate to use the paired difference t-test? The owner of a bottling company is considering buying a new bottling machine. He has been testing two different machines that are being considered. After collecting 300 samples from each machine over several weeks, he was able to conduct a two sample z test.

He decided to utilize a 0.05 significant level for the test. The test was to address the claim that the mean weight of the bottles filled by the Orno machine was greater than the mean weight of the bottles filled by the Edne machine. The test statistics was 2.21. What is the decision regarding the hypothesis? Two different accounting procedures that are utilized by businesses as a way to evaluate their inventory are LIFO (Last In First Out) and FIFO (First In First Out). ABC manufacturer evaluated its finished goods inventory (in $ thousands) for five products using both procedures. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? Product FIFO (F) LIFO (L) 1 225 221 2 119 100 3 100 113 4 212 200 5 248 245 The 5% level of significance was selected for the t value. The calculated test statistic was 1.93. What is the decision? You are conducting a two-tailed test of means, but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is A consumer researcher is testing the difference between two proportions at the 0.05 level of significance. The researcher was utilizing the z distribution for the test. If the computed test statistic z value was 1.12, what was the decision? Watsons TV claims that their televisions have the best performance record on the market. They advertise that after 3 years only 10% of their sold televisions have had any type of repairs. The president of the company wanted to confirm that this statement was correct. To do this, a sample of 60 sets was taken of sets that had been sold and were at least 3 years old. Twelve percent of these television sets had been in for repair. The null hypothesis is that there is no difference between the stated percent and the sample data. At the .05 significant level, what can we conclude about the null hypothesis? The accountant for Thomass Furniture Store is concerned regarding the outstanding receivable owed the company. There has been a cash flow problem and it is believed that the slow collection of accounts receivable is partially the blame. The accountant believes that 40% of the present accounts are more than 4 months behind in making payments. To be able to make a decision regarding this belief, a random sample of 100 accounts was taken. It was found that 37 accounts were more than 4 months late. Did the sample data confirm the accountants belief? Use the .05 significant level for the statistical test. New college business graduates are finding it difficult to get a job. A business journal has reported that only one in five graduates is able to find a job within 6 months of their graduation. A report by the University of Phoenix indicated that out of a survey of 300 recent business graduates, 75 had jobs. You are a business major at the University of Phoenix and have a concern about getting a job. Based on this data, will a graduate of the University of Phoenix have a better chance of getting a job in the first 6 months after graduation? Use the .05 significant level for the test. Which is NOT a valid assumption for the utilization of the ANOVA test? In the metro area there are four major supermarket chains. To determine if there was a difference between these stores, regarding their pricing of food, a consumer group did a test. In the Eastgate area of town, each of the supermarket chains has a store. Twenty-five common household items were selected for the test. These items were purchased at each of the four stores and the prices were compared. To analyze this data, what would be the best statistical test to use? The F distribution is utilized with the ANOVA test. There are some basic assumptions associated with the distribution. Which of these assumptions is NOT valid? If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? Robinson, a large department store, wanted to example to look at which credit cards were being utilized for purchases. A sample of 18 credit card sales was taken and recorded. The amounts charged for each of three different credit cards, MasterCard, Visa, and Discover, were: six MasterCard sales, seven Visa sales, and five Discover sales. The store used an ANOVA to test if the mean sales for each credit card were equal. What are the degrees of freedom for the F statistic? Ace Car Rental has three main models that are used in it midsize range of cars. The cars are very similar and perform at about the same level. Since the customer has to pay for the gas use during the rental period, the manager is often asked about which car gets the best gas mileage. To be able to address this question, an analysis was done of the three makes of cars. Each car can use any one of four different grades of gasoline. The data collected was for each car for each type of fuel. Performance was measured in miles per gallon. Perform an ANOVA test and state the results. Gasoline Model A Model B Model C Regular 21.4 22.3 20.8 Super Regular 20.6 17.1 19.5 Unleaded 21.3 19.2 20.2 Premium 20.5 20.3 18.5 Which of the following values of Spearman's (rho) indicates the strongest relationship between two variables? In the chi-squared goodness-of-fit test, if the expected frequencies ei and the observed frequencies fi were quite different, we would conclude that the [ID: 29826] Of the values for a chi-squared test statistic listed below, which one is most likely to lead to rejecting the null hypothesis in a goodness-of-fit test? The city of Denver has several golf courses around the city. The Recreational Park manager is trying to set the schedule for the employees at these courses. His concern is that he wants to have enough staff to handle the daily demands but to not be overstaffed. He has concerns about the next years budget and is trying to curb expenses where possible. To be able to make a decision regarding staffing, he collected data regarding the number of rounds of golf played during the week. The weekend was excluded because the weekends are always very busy. He wanted to see if there was a significant difference between the days of the week in terms of rounds being played. If there was a difference, then he could use this information to help make staffing decisions. The result of the data collection is as follows: Day of Week Rounds Monday 150 Tuesday 90 Wednesday 120 Thursday 100 Friday 140 What is the result of the statistical test? Can the managers staff schedule vary for different days of the week? Use the chi square distribution at the .05 significant level. The Ohio Department of Highways is in the process of selecting a new paint for highway use. Four different paint companies have been contact regarding this need and each of the companies has supplied paint for testing. Before deciding the winner of the new contract, a test was conducted to determine which paint was the best, in terms of how long it would last. The results of the test are as follows: Category Paint A Paint B Paint C Paint D Days 345 320 350 310 Each paint is expected to last 330 days. Is there a significant difference between these four paints? Use the chi square distribution at the .05 significant level to answer this question. Seamens Manufacturing has five hundred employees at its plant. These employees are divided into three main groups: administration, clerical, and labor. The company is looking at making some changes to it retirement plan that is available for employees. There are three plans beginning considered. The 500 employees were surveyed regarding their preferences for the various retirement plans. The president is concerned if there is a relationship between the person position in the company and which retirement plan was preferred. Utilize the chi square distribution at the .05 significant level, and determine if there is a relationship between position in company and the retirement plan selected. Position Plan A Plan B Plan C Labor 170 50 30 Clerical 30 110 30 Administration 20 20 40 What is your decision regarding the differences between the observed and expected frequencies if the critical value of chi-square is 7.815 and the computed value is 6.789? Cornys Feed Company markets four different mixtures of feed for chickens. These feeds have different combinations of ingredients. One question that the manager is often asked by customers is if there is a difference between the four feeds in terms of weight gain. To be able to address this question an analysis was done of the four feeds. They contacted a local farmer to conduct a test regarding the four feeds. There were 28 chickens selected for the test. These chickens were divided into four groups, with each group receiving one of the feeds. The statistical test selected for the analysis was the Kruskal-Wallis test and the .05 significant level was used for the test. The test result was H 4.65. This indicates that The Big Toy House is a local company that specializes in selling children outdoor playhouses. With many businesses there is a certain amount of difficulty in collecting money on past due accounts. This has become a concern of the owner. A recent trade magazine indicated that the national averages for account receivable were: 65% current, 25% late, and 10% not collectable. A recent study of the companys records indicated that 60 percent of the account receivable is current. Thirty percent of the accounts were late and the remaining 10% of receivable were viewed as being not collectable. To determine if his store was in-line with the national average, the manager had a statistical analysis performed. The chi square test was selected for the analysis and the .05 significant level was used. The test statistics was X² = 6.725. What is the correct decision regarding this result? What is the measure that indicates how precise a prediction of Y is based on X or, conversely, how inaccurate the prediction might be? A simple linear regression generated a correlation coefficient of 0.01. This tells us that What is the variable used to predict another variable called? Smiths Appliances is evaluating its advertising budget. The owner is trying to decide if the budget needs to be altered or not. The question: Is there a positive return on the investment that is being made in advertising? What is the relationship between sales and the amount spent on advertising? The owner collected data for the past year by month. The data is in millions of dollars. Month Advertising Expense Sales Revenue January 2 4 February 3 5 March 3 6 April 5 8 May 6 8 June 4 7 July 5 7 August 6 8 September 7 9 October 8 10 November 10 13 December 9 11 Is there a relationship between the two variables? What is the coefficient of correlation for this data? In Chicago there are several large entertainment complexes. These entertainment complexes are important components of the overall citys makeup. Having these complexes to do well is advantageous to the city. The Chamber of Commerce wanted to determine the relationship between total revenue and profit, in billions of dollars, of 10 complexes. The data that was collected is as follows: Company Revenue Profit Company Revenue Profit A 1.562 0.762 F 4.526 2.543 B 7.651 2.343 G 1.891 .0876 C 2.231 0.231 H 3.564 2.789 D 1.879 1.102 I 3.213 3.134 E 8.345 3.546 J 2.432 4.451 Calculate the coefficient of correlation for these two variables. The Golden Park and Recreation Department wants to determine a better way to estimate income at the various recreational centers. One relationship that was investigated was between family size and amount spent on recreation. The question was if smaller families spent less money than larger families. A regression analysis tool was selected to be used to address this question. Data was collected from 15 member families regarding what they spent each week on recreation. Their data was as follows: Family Size Amount Spent Family Size Amount Spent Family Size Amount Spent 4 $109 3 $101 3 $115 5 114 4 120 6 174 3 161 4 125 5 156 5 159 6 170 4 145 5 164 3 104 5 145 Compute the coefficient of correlation. In the least squares equation, Y' = 12 + 25X the value of 25 indicates The least squares regression equation is Y' = 1312 + 245X. When X = 5, what does Y' equal? When an insurance company is going to write a new home owner policy, one concern is the distance between the house and the nearest fire department station. This is one factor that goes in to determining the cost of the insurance for the home owner. ETB Insurance Company wants to determine if there is a relationship between the distance to a fire station and the amount of fire damage to a house. A random sample of 50 claims was selected for analysis. The correlation coefficient was 0.78. Which is the correct interpretation and recommendation? Multiple regression analysis assumes or requires that If the net regression coefficients in the population are significantly different from zero, what can be included? If there are four independent variables in a multiple regression equation, there are also four Given the trend equation Y' = 24 + 0.6t (base year = 2006), what would be the forecast value for 2010? If a quarterly seasonal index is 0.66, it implies that The time series component that reflects variability over short, repetitive time periods that last less than one year is called Midwest State University Office of Registrar is reviewing the universitys enrollment for the past 10 years. It is know that there are seasonal variable that affects the universitys enrollment. To be better able to address business decisions that are affected by enrollment, an analysis of data was necessary. The school operates on a quarter system of enrollment starting typically with fall quarter and ending with summer quarter. The analysis of the data produced these four quarterly indexes. Fall Winter Spring Summer 1.2617 1.1896 1.040 0.4447 Which statement is correct based on this analysis? Big House Lumber Company, located in Dayton, Ohio, is preparing its annual business report. The manager has performed an analysis of the business annual sales starting in 2004 and concluding with 2009. This analysis produced an annual sales linear trend equation of Y' = 10.0989 + 0.14213t. The manager has been indicating to the companys investors that sales in 2011 will exceed $11.5 million dollars. Is the manager statement accurate? An analysis of graduates from a local business college was performed to determine if there was a relationship between GPA and starting salary of recent graduates. It was believed that a higher GPA would result in a higher starting salary. The analysis of data collected from recent graduates produced the following correlation matrix. Salary GPA 0.902 Business 0.911 0.851 Which statement is correct regarding the interpretation of the analysis? The statement that determines if the null hypothesis is rejected or not is called the What are the critical z-values for a two-tailed hypothesis test if the significant level = 0.01? An independent consumer testing lab preformed a statistical test on 25 type-C alkaline batteries and calculated the mean life for a particular use before they failed was 22.5 hours. The distribution of the lives approximated a normal distribution. The standard deviation of the distribution was 1.1 hours. Information on the package states that the batteries should last 24 hours. The test question was if this difference between the test statistics and the stated life of the battery was significant? The .05 significant level was selected for the test. Which is the correct statement? K & S Construction, located in Phoenix, Arizona, is working on its business plan for the upcoming year. They did a study to determine if they should focus on building condominiums or individual houses. A building study, which had been conducted by the state, indicated that 60 percent of those families looking to buy a home in Arizona desired to buy a condominium. K & S Construction wanted to know if this figure applied to Phoenix. They collected a sample of 500 individuals that had expressed plans to buy a new home. The z-distribution was selected for this proportion test. The null hypothesis is p = 0.60 and the alternate is p ? 0.60. The significant level selected was .05. From the sample of 500, it was determined that 290 wanted to buy a condominium. What decision should be made regarding the null hypothesis? In classical hypothesis testing, the test statistic is to the critical value what the ________________. A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test she wished to perform might have unacceptable large possibilities of Type II error, ß. Which of the following would solve this problem? Thomas Delivery has a fleet of 24 trucks that are utilized for the companies; business. Electro-Lite, a manufacturer of spark plugs, claims that its spark plugs have an average life in excess of 25,000 miles. The purchasing agent at Thomas Delivery purchased 24 sets and found that the sample average life was 26,300 miles, the sample standard deviation was 1,500 miles, and the computed test statistic was t = 3.423. Based on these findings, at the 0.05 level, is there enough evidence to accept the manufacturer's claim? A machine is set to fill the small size packages of Good and Better candies are packaged with 60 pieces of candies in each bag. Sampling results revealed: 3 bags of 61, 2 bags of 59, 1 bag of 58, and 2 bags of 62. How many degrees of freedom are there? If the paired differences are normal in a test of mean differences, then the distribution used for testing is the Golf balls that are properly manufactured will have a rebound height of 42 inches when dropped by a testing machine from a height of 5 feet. The quality control inspector is concerned that a new manufacturing machine is not properly calibrated and that the resulting golf balls are falling short of the desired height. At random, 100 golf balls were selected for a test. The test results indicated that the rebound height was 41.6 inches with a standard deviation of 0.5. At the .05 significant level, what is the result of the test? A recent study by College Stat Company reported a nationwide survey of college students determined that students spend 2 hours studying for each hour in the classroom. Professor Baker at State College wants to determine whether the time students spend at her college is significantly different from the national average of 2 hours. A random sample of 20 statistics students resulted in an average of 1.75 hours with a standard deviation of 0.24 hours. A t-test was conducted at the 5% level of significance. The calculated value of t was -4.03. What was Professor Baker decision? In a test for the equality of two variances (two-tailed), when the populations are normal, a 5% level of significance was used. Sample sizes were n1 = 13 and n2 = 10. The upper critical value for the test is When is it appropriate to use the paired difference t-test? The owner of a bottling company is considering buying a new bottling machine. He has been testing two different machines that are being considered. After collecting 300 samples from each machine over several weeks, he was able to conduct a two sample z test.

He decided to utilize a 0.05 significant level for the test. The test was to address the claim that the mean weight of the bottles filled by the Orno machine was greater than the mean weight of the bottles filled by the Edne machine. The test statistics was 2.21. What is the decision regarding the hypothesis? Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? Product FIFO (F) LIFO (L) 1 225 221 2 119 100 3 100 113 4 212 200 5 248 245 The 5% level of significance was selected for the t value. This example is what type of test? You are conducting a two-tailed test of means, but your software package only calculates a one-tailed p-value equal to 0.13. The actual p-value for your test is A consumer researcher is testing the difference between two proportions at the 0.05 level of significance. The researcher was utilizing the z distribution for the test. If the computed test statistic z value was 1.12, what was the decision? What is the critical value for a one-tailed hypothesis test in which a null hypothesis is tested at the 5% level of significance based on two samples, both sample sizes are 13? Watson's TV claims that their televisions have the best performance record on the market. They advertise that after 3 years only 10% of their sold televisions have had any type of repairs. The president of the company wanted to confirm that this statement was correct. To do this, a sample of 60 sets was taken of sets that had been sold and were at least 3 years old. Twelve percent of these television sets had been in for repair. The null hypothesis is that there is no difference between the stated percent and the sample data. At the .05 significant level, what can we conclude about the null hypothesis? A trolley system is being planned for the downtown area of Cincinnati, Ohio. To be able to proceed with this project, planners have indicated that at least 20% of the residents of the areas that would be covered need to support the idea. To determine the feelings of these city residents, a sample of 300 residents was taken. Seventeen percent of the sample responded that they would ride the trolley. Is this enough evidence for the project to proceed? Use the .05 level of significant. New college business graduates are finding it difficult to get a job. A business journal has reported that only one in five graduates is able to find a job within 6 months of their graduation. A report by the University of Phoenix indicated that out of a survey of 300 recent business graduates, 75 had jobs. You are a business major at the University of Phoenix and have a concern about getting a job. Based on this data, will a graduate of the University of Phoenix have a better chance of getting a job in the first 6 months after graduation? Use the .05 significant level for the test. Blake's Mortgage Company utilizes four different appraisers for the purpose of determining the value of a house. There is a concern by the company's owner that the appraisers are not providing the same estimates. She wants to determine if there is a difference between the four appraisers. Six houses were selected and each appraiser provided an appraisal for each of the six houses. What would be the best statistical test to use for the analysis of this data? Analysis of variance is used to The F distribution is utilized with the ANOVA test. There are some basic assumptions associated with the distribution. Which of these assumptions is NOT valid? If an ANOVA test is conducted and the null hypothesis is rejected, what does this indicate? In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by Each Christmas season there is a hot toy that everyone must have, especially if you are under the age of nine. This prized toy can be purchased at many different types of stores. A consumer group wanted to determine if there was a difference in price for the toy depending on where the toy was purchased. Is the price of this toy the same for the different stores or is there a difference? In the Cincinnati area there are three main stores of concern: Wal-Mart, Meijer, and Toys R Us. Data was collected from different stores around the city. Prices will vary depending on the location of the store. The collected data is as follows (in dollars): Wal-Mart Meijer Toys R Us 15 18 20 12 17 19 12 14 16 14 15 20 13 17 19 Conduct an ANOVA analysis of the data. Is there a significant difference between the three stores? The chi-square distribution becomes more symmetrical as What nonparametric test is used when the assumptions for the parametric analysis of variance (ANOVA) cannot be met? Its purpose is to test whether three or more populations are equal. The data must be at least ordinal scaled. In the chi-squared goodness-of-fit test, if the expected frequencies ei and the observed frequencies fi were quite different, we would conclude that the [ID: 29826] The nonparametric counterpart of the randomized block model of the ANOVA is the Seamen's Manufacturing has five hundred employees at its plant. These employees are divided into three main groups: administration, clerical, and labor. The company is looking at making some changes to it retirement plan that is available for employees. There are three plans beginning considered. The 500 employees were surveyed regarding their preferences for the various retirement plans. The president is concerned if there is a relationship between the person position in the company and which retirement plan was preferred. Utilize the chi square distribution at the .05 significant level, and determine if there is a relationship between position in company and the retirement plan selected. Position Plan A Plan B Plan C Labor 170 50 30 Clerical 30 110 30 Administration 20 20 40 The Ohio Department of Highways is in the process of selecting a new paint for highway use. Four different paint companies have been contact regarding this need and each of the companies has supplied paint for testing. Before deciding the winner of the new contract, a test was conducted to determine which paint was the best, in terms of how long it would last. The results of the test are as follows: Categor Paint A Paint B Paint C Paint D Days 345 320 350 310 Each paint is expected to last 330 days. Is there a significant difference between these four paints? Use the chi square distribution at the .05 significant level to answer this question. To determine whether four population means are equal, a sample from each population was selected at random and using the Kruskal-Wallis test, H was computed to be 2.11. What is your decision at the 0.05 level of risk? State Insurance Company believes that the age of the driver and number of accidents that occurs are related. The feeling is that younger drivers are more careless and will have more accidents. The claims department wants to determine if this line of thinking is correct. To answer this question a random sample of 1500 policyholders was investigated. A chi square analysis was performed on the data at the .05 significant level. The analysis produced a chi square value of 47.56. What is the correct decision regarding the null hypothesis that whether a claim is filed and the age of the policyholder are not related? Corny's Feed Company markets four different mixtures of feed for chickens. These feeds have different combinations of ingredients. One question that the manager is often asked by customers is if there is a difference between the four feeds in terms of weight gain. To be able to address this question an analysis was done of the four feeds. They contacted a local farmer to conduct a test regarding the four feeds. There were 28 chickens selected for the test. These chickens were divided into four groups, with each group receiving one of the feeds. The statistical test selected for the analysis was the Kruskal-Wallis test and the .05 significant level was used for the test. The test result was H 4.65. This indicates that A simple linear regression generated a correlation coefficient of 0.01. This tells us that What is the variable used to predict another variable called? What does a coefficient of correlation of 0.70 infer? A researcher was investigating the relationship between the variables grades in high school and grades in college. The investigator wanted to determine if a relationship existed and if so, to what extent. A regression analysis was perform on the data and the correlation value was r = .71. Based on this finding, which statement is correct? The Ohio Electric Company is investigating electric consumption by single family homes based on the number of rooms. The investigators wanted to determine the relationship between number of rooms and electric consumption in kilowatt-hours (thousands). A sample of 12 homes was selected and the data is as follows: Number of Rooms Kilowatt-Hours Number of Rooms Kilowatt-Hours 10 10 8 9 9 8 10 11 7 6 10 9 12 13 8 9 8 7 6 7 11 12 5 6 What percent of the variation is explained by the variable, number of rooms? Smith's Appliances is evaluating its advertising budget. The owner is trying to decide if the budget needs to be altered or not. The question: Is there a positive return on the investment that is being made in advertising? What is the relationship between sales and the amount spent on advertising? The owner collected data for the past year by month. The data is in millions of dollars. Month Advertising Expense Sales Revenue January 2 4 February 3 5 March 3 6 April 5 8 May 6 8 June 4 7 July 5 7 August 6 8 September 7 9 October 8 10 November 10 13 December 9 11 Is there a relationship between the two variables? What is the coefficient of correlation for this data? The least squares regression equation is Y' = 1312 + 245X. When X = 5, what does Y' equal? When an insurance company is going to write a new home owner policy, one concern is the distance between the house and the nearest fire department station. This is one factor that goes in to determining the cost of the insurance for the home owner. ETB Insurance Company wants to determine if there is a relationship between the distance to a fire station and the amount of fire damage to a house. A random sample of 50 claims was selected for analysis. The correlation coefficient was 0.78. Which is the correct interpretation and recommendation? The Actuarial Department of an insurance company was assigned the task of determining the relationship between the distance to a fire station and the amount of damage to a house. This is one factor that is utilized in determining the cost of insurance for a home owner. A sample of 35 claims was selected from last year. When the analysis was completed the following regression equation was the result. (X is the distance to a fire station and Y' is the amount of damage in thousands of dollars) Y' = 11.65 + 5.12X If a house was 10 miles from the fire station, what would be the best estimate of the cost of damages to the house? Conducting a multiple regression analysis, the residual analysis is used to test the requirement that In a multiple regression ANOVA table, explained variation is represented by If there are four independent variables in a multiple regression equation, there are also four If the least squares equation for Mary's Clothing sales data from 2004 to 2008 is represented by the equation Y' = 12 + 1.1t (in $ millions). What is the value of t and the forecast for 2010? The time series component that reflects variability over short, repetitive time periods that last less than one year is called Given the trend equation Y' = 24 + 0.6t (base year = 2006), what would be the forecast value for 2010? The owner of a local construction company that specializes in outdoor structures desires to make a prediction regarding the next business year sales. Expansion of the business is one possible decision that could be made. It has been determined that the business needs to be at least $8 million dollars in annual sales before expansion could be considered. The following is data for the past 6 years. (Sales in millions of dollars.) Year Sales Year Sales 2004 7.45 2007 7.94 2005 7.83 2008 7.76 2006 8.07 2009 7.90 The statistical analysis of the data produced this least square trend equation. Y' = 7.634 + 0.05457t What should the owner's decision be regarding expansion in 2010? Midwest State University Office of Registrar is reviewing the university's enrollment for the past 10 years. It is know that there are seasonal variable that affects the university's enrollment. To be better able to address business decisions that are affected by enrollment, an analysis of data was necessary. The school operates on a quarter system of enrollment starting typically with fall quarter and ending with summer quarter. The analysis of the data produced these four quarterly indexes. Fall Winter Spring Summer 1.2617 1.1896 1.1040 0.4447 Which statement is correct based on this analysis? Big House Lumber Company, located in Dayton, Ohio, is preparing its annual business report. The manager has performed an analysis of the business annual sales starting in 2004 and concluding with 2009. This analysis produced an annual sales linear trend equation of Y' = 10.0989 + 0.14213t. The manager has been indicating to the company's investors that sales in 2011 will exceed $11.5 million dollars. Is the manager statement accurate? What is the critical value for a two-tail, one sample hypothesis test in which a null hypothesis is tested at the 5% level of significance based on a sample size of 23? The normally distributed AAA battery life is stated to be 350 days when used in a clock radio. The Big Charge Battery Company has recently modified the AAA batteries so as to extent their life. The owner of the company wanted to know if the improved batteries really did last significantly longer. A sample of 100 of the improved batteries was tested. It was discovered that the mean life was 362 days and the sample standard deviation was 10 days. The research department decided to conduct the test at the 0.05 level of significance whether the modification actually increased the life of the AAA battery. What was their decision rule? What are the critical z-values for a two-tailed hypothesis test if the significant level = 0.01? K & S Construction, located in Phoenix, Arizona, is working on its business plan for the upcoming year. They did a study to determine if they should focus on building condominiums or individual houses. A building study, which had been conducted by the state, indicated that 60 percent of those families looking to buy a home in Arizona desired to buy a condominium. K & S Construction wanted to know if this figure applied to Phoenix. They collected a sample of 500 individuals that had expressed plans to buy a new home. The z-distribution was selected for this proportion test. The null hypothesis is p = 0.60 and the alternate is p ? 0.60. The significant level selected was .05. From the sample of 500, it was determined that 290 wanted to buy a condominium. What decision should be made regarding the null hypothesis? A statistician was setting up a hypothesis test with a level of significance dictated by upper management. However, she was concerned that the test she wished to perform might have unacceptable large possibilities of Type II error, ß. Which of the following would solve this problem? Doi Winery has two wine shops in the neighboring towns of Seamen and Batavia. The favorite wine, as advertised, is Raspberry wine. A survey of 300 customers at the Seamen store revealed that 225 individuals preferred the Raspberry wine while 290 out of 400 in Batavia preferred the same flavor. To test the hypothesis that there was no difference in preferences in the two towns, what is the alternate hypothesis? Cake manufacturer Little Divas wants to increase the shelf life of its easy-to-fix cupcake mixes. Companys records indicate that the average shelf life of the mix is 230 days. A new, improved cupcake mix was developed and a sample of 10 boxes of the cupcake mix had these shelf lives (in days): 231, 233, 232, 233, 228, 231, 234, 229, 235, and 232. If the standard deviation was .67 and at the 0.025 significant level, has the shelf life of the cupcake mix increased? A machine is set to fill the small size packages of Good and Better candies are packaged with 60 pieces of candies in each bag. Sampling results revealed: 3 bags of 61, 2 bags of 59, 1 bag of 58, and 2 bags of 62. How many degrees of freedom are there? If the paired differences are normal in a test of mean differences, then the distribution used for testing is the Newtons, a tire manufacturer, wanted to set a mileage guarantee on its new Road Warrior 60 tire. A sample test of 500 tires revealed that the tires mileage is normally distributed with a mean of 50,000 miles and a standard deviation of 1,750 miles. The warranty on the tires is presently set at 47,500 miles. The z-test statistic result was 1.43. The manufacturer wanted to determine if the tires were exceeding the guarantee. At the .05 significant level, it was concluded that the tires are exceeding the manufacturers guarantee. Flash Jolt, a manufacturer of camera equipment, annually introduces new models in the fall of the year. At the conclusion of the Christmas season, retail dealers are contacted regarding their stock on hand of each piece of equipment. It has been discovered that unless 47% of the new equipment ordered by the retailers in the fall had been sold by Christmas, immediate production cutbacks are needed. At the end of the 2009 Christmas shopping season a survey of 100 dealers indicated that 45% of Flash Jolt equipment had been sold. It was decided to continue production levels at the current levels. The statistical test was conducted at the 0.05 level. Computed z = 0.40. In a test for the equality of two variances (two-tailed), when the populations are normal, a 5% level of significance was used. Sample sizes were n1 = 13 and n2 = 10. The upper critical value for the test is Indy H2O is a water bottling company. They are looking at two different bottling manufacturers equipment for the purpose of replacing some old equipment. The net weights of a sample of bottles filled by a machine manufactured by WTR, and the net weights of a sample filled by a similar machine manufactured by Target are (in grams): WTR: 8, 9, 7, 8, 9, and 10 Target: 8, 10, 7, 11, 9, 12, 8, and 9 Testing the claim at the 0.05 level that the mean weight of the bottles filled by the Target machine is greater than the mean weight of the bottles filled by the WTR machine, what is the critical value? Accounting procedures allow a business to evaluate their inventory at LIFO (Last In First Out) or FIFO (First In First Out). A manufacturer evaluated its finished goods inventory (in $ thousands) for five products both ways. Based on the following results, is LIFO more effective in keeping the value of his inventory lower? Product FIFO (F) LIFO (L) 1 225 221 2 119 100 3 100 113 4 212 200 5 248 245 The 5% level of significance was selected for the t value. This example is what type of test? When is it appropriate to use the paired difference t-test? If the paired differences are normal in a test of mean differences, the distribution used for testing is the A consumer researcher is testing the difference between two proportions at the 0.05 level of significance. The researcher was utilizing the z distribution for the test. If the computed test statistic z value was 1.12, what was the decision? When testing for differences between two means, the Behrens-Fisher problem arises when the sample populations are The accountant for Thomass Furniture Store is concerned regarding the outstanding receivable owed the company. There has been a cash flow problem and it is believed that the slow collection of accounts receivable is partially the blame. The accountant believes that 40% of the present accounts are more than 4 months behind in making payments. To be able to make a decision regarding this belief, a random sample of 100 accounts was taken. It was found that 37 accounts were more than 4 months late. Did the sample data confirm the accountants belief? Use the .05 significant level for the statistical test. Watsons TV claims that their televisions have the best performance record on the market. They advertise that after 3 years only 10% of their sold televisions have had any type of repairs. The president of the company wanted to confirm that this statement was correct. To do this, a sample of 60 sets was taken of sets that had been sold and were at least 3 years old. Twelve percent of these television sets had been in for repair. The null hypothesis is that there is no difference between the stated percent and the sample data. At the .05 significant level, what can we conclude about the null hypothesis? A trolley system is being planned for the downtown area of Cincinnati, Ohio. To be able to proceed with this project, planners have indicated that at least 20% of the residents of the areas that would be covered need to support the idea. To determine the feelings of these city residents, a sample of 300 residents was taken. Seventeen percent of the sample responded that they would ride the trolley. Is this enough evidence for the project to proceed? Use the .05 level of significant. Blakes Mortgage Company utilizes four different appraisers for the purpose of determining the value of a house. There is a concern by the companys owner that the appraisers are not providing the same estimates. She wants to determine if there is a difference between the four appraisers. Six houses were selected and each appraiser provided an appraisal for each of the six houses. What would be the best statistical test to use for the analysis of this data? In the metro area there are four major supermarket chains. To determine if there was a difference between these stores, regarding their pricing of food, a consumer group did a test. In the Eastgate area of town, each of the supermarket chains has a store. Twenty-five common household items were selected for the test. These items were purchased at each of the four stores and the prices were compared. To analyze this data, what would be the best statistical test to use? Mr. Thomas owns three different restaurants in Cincinnati, Ohio. He is concerned about the profitability of the restaurants. There are monthly differences between the restaurants and he wants to determine if the differences in profit are significant. Mr. Thomas wants to do a statistical test to see if he should be concerned. The best test to address this problem would be In ANOVA analysis, when the null hypothesis is rejected, we can find which means are different by Ace Car Rental has three main models that are used in it midsize range of cars. The cars are very similar and perform at about the same level. Since the customer has to pay for the gas use during the rental period, the manager is often asked about which car gets the best gas mileage. To be able to address this question, an analysis was done of the three makes of cars. Each car can use any one of four different grades of gasoline. The data collected was for each car for each type of fuel. Performance was measured in miles per gallon. Perform an ANOVA test and state the results. Gasoline Model A Model B Model C Regular 21.4 22.3 20.8 Super Regular 20.6 17.1 19.5 Unlea

RES 342

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Answered by maddy 7 years ago

**Excerpt from file: **Math Tutorial RES 342 Final Exam An independent consumer testing lab preformed a statistical test on 25 type-C alkaline batteries and calculated the mean life for a particular use before they failed was 22.5 hours. The distribution of the lives approximated a normal distribution. The standard

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