Asked by maddy 3 months ago

In this exercise, we will examine the attitudes of liberals and conservatives toward affirmative action policies in the workplace. Data from the 2010 683 reveal that 12% of conservatives (N = 336) and 27% of liberals (N = 267) indicate that they “strongly support” or “support” affirmative action policies for African Americans in the workplace.

a. What is the appropriate test statistic? Why?

b. Test the null hypothesis with a one-tailed test (conservatives are less likely to support affirmative action policies than liberals); $\alpha$ = .05. What do you conclude about the difference in attitudes between conservatives and liberals?

c. If you conducted a two-tailed test with $\alpha$ = .05, would your decision have been different?

difference proportions

test statistic

Answered by maddy 3 months ago

**a)** Asks what the appropriate test statistics is. We are comparing proportions of two samples in this case, so we would use a test statistic that is the difference of proportions. So use the following:

$$Z = \frac{p_1-p_2}{S_{p_1-p_2}} $$

where,

$$S_{p_1-p_2} = \sqrt{\frac{p_1(1-p_1)}{N_1}+\frac{p_2(1-p_2)}{N_2}}$$

**b)** We are using a one tailed test. First write down your null and alternative hypothesis, and our knowns in this problem:

$$H_0: p_1=p_2$$ $$H_a: p_1 \lt p_2$$ $$p_1=0.12, \; p_2=0.27, \; N_1=336, \; N_2=267$$

Plugging these values into the above formula yields the result,

$$S_{p_1-p_2} = \sqrt{\frac{0.12(1-0.12)}{336}+\frac{0.27(1-0.27)}{267}} \approx 0.3$$

$$Z = \frac{0.12-0.27}{0.3}=-5$$

finding the p-value for this by looking in a standard normal table and we see that p is much less than alpha, or in mathematical notation,

$$P(Z \lt -5) \lt \alpha$$

So reject the null hypothesis. There is a difference between conservatives and liberals in support for affirmative action.

**c)** For a two tailed test we just double the p-value we found in part b. But the p-value is so small for $Z \lt -5$ that we still reject the null under these circumstances - so the conclusion is the same.

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Asked: 3 months ago