In this exercise, we will examine the attitudes of liberals and conservatives toward affirmative action

# In this exercise, we will examine the attitudes of liberals and conservatives toward affirmative action

398.7k points

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

398.7k points

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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