STAT 167 Week 4
Week 4 Individual Assignment Distribution, Hypothesis Testing, and Error Worksheet 1. Describe a normal distribution in no more than 100 words (0.5 point). 2. Construct a normal quantile plot in Statdisk, show the regression line, and paste the image into your response. Based on the normal quantile plot, does the data above appear to come from a population of Bigcone Douglasfir tree ages that has a normal distribution? Explain (0.5 point). 3. Calculate the sample mean and standard deviation for the age of Bigcone Douglasfir trees based on the data above. If this accurately represents the population mean and standard deviation for the age of surviving Bigcone Douglasfir trees in the burn area, what is the probability that a randomly selected surviving Bigcone Douglasfir tree from the burn area will be 111 years old or less? Round to the nearest hundredth (0.5 point). 4. Calculate the sample mean and standard deviation for the age of Bigcone Douglasfir trees based on the data above. If this accurately represents the population mean and standard deviation for the age of surviving Bigcone Douglasfir trees in the burn area, what is the probability that a randomly selected surviving Bigcone Douglasfir tree from the burn area will be less than 0 years old? Round to the nearest hundredth. Based on this result, is it logical to assume that the population of age of surviving Bigcone Douglasfir trees in the burn area is normally distributed with the parameters identified. Why or why not (0.5 point)? 5. Describe a standard normal distribution in no more than 100 words (0.5 point). 6. In a standard normal distribution, what is the probability of randomly selecting a value between 2.555 and 0.745? Round to four decimal places (0.5 point). 7. Describe a uniform distribution in no more than 100 words (0.5 point). 8. Describe the sampling distribution of the mean in no more than 100 words (1 point). 9. Explain the central limit theorem in no more than 150 words (1 point). 10. Describe the z distribution in no more than 100 words (0.5 point). 11. Explain when the z distribution can be used in no more than 150 words (0.5 point). 12. Describe the t distribution in no more than 100 words (0.5 point). 13. Explain when the t distribution can be used in no more than 150 words (0.5 point). 14. Describe the chisquare distribution in no more than 100 words (0.5 point). 15. Explain when the chisquare distribution can be used in no more than 150 words (0.5 point). 16. Determine the appropriate approach to conduct a hypothesis test for this claim: Fewer than 5% of patients experience negative treatment effects. Sample data: Of 500 randomly selected patients, 2.2% experience negative treatment effects (0.5 point). 17. Determine the appropriate approach to conduct a hypothesis test for this claim: The systolic blood pressure of men who run at least five miles each week varies less than does the systolic blood pressure of all men. Sample data: n = 100 randomly selected men who run at least five miles each week, sample mean = 108.4, and s = 20.3 (0.5 point). 18. Determine the appropriate approach to conduct a hypothesis test for this claim: The mean sodium content of a 30 g serving of snack crackers is 2,200 mg. Sample data: n = 130 snack crackers, sample mean = 3,100 mg, and s = 570. The sample data appear to come from a normally distributed population (0.5 point). 19. Describe a type I error in no more than 100 words (0.5 point). 20. List two strategies that can minimize the likelihood of a type I error (0.5 point). 21. Describe a type II error in no more than 100 words (0.5 point). 22. List two strategies that can minimize the likelihood of a type II error (0.5 point). 23. In a 250 to 350word essay, compare type I and type II errors and explain the possible negative effects of each error type in the life sciences (2 points).
Team Assignment Confidence Intervals in the Life Sciences Presentation
Discussion Questions Explain, as if to a high school student, what it means to make a type I error. Then, in the same way, explain what it means to make a type II error. Can you find a realworld example where a type I or type II error would most likely skew the interpretations of a study? Is there a way for scientists to correct for these errors? Why or why not? Next, reply to a classmate’s response and ask a question about the response that you think a high school student would ask.
Explain the circumstances under which a z distribution should be constructed. Under what circumstances should a t distribution be constructed? When can neither a z nor a t distribution be constructed? Provide an example from a particular life science for each of these instances. Next, reply to the response of a classmate with examples from a different life science that you provided and comment on the similarities and differences in the data from different life sciences.
