Question

In 2016, the Pew Research Center16 surveyed 1,799 white and 1,001 black Americans about their views on race and inequality. Pew researchers found “profound differences between black and white adults in their views on racial discrimination, barriers to black progress and the prospects for change.” White and black respondents also disagreed about the best methods to achieve racial equality. For example, 34% of whites and 41% of blacks said that “bringing people of different racial backgrounds together to talk about race” would be a very effective tactic for groups striving to help blacks achieve equality. Test whether the proportion of white respondents who support this tactic is significantly less than the proportion of black respondents. State the null and research hypotheses. Calculate the Z statistic and test the hypothesis at the .05 level. What is your Step 5 decision?

Answer 1

n1 = 1799

n2 = 1001

= 0.34

= 0.41

Claim: The proportion of white respondents who support this tactic is significantly less than the proportion of black respondents.

The null and alternative hypothesis is

Level of significance = 0.05

Test statistic is

Critical value = 1.64 ( Using z table)

| z | > 1.64 we reject null hypothesis.

Conclusion: the proportion of white respondents who support this tactic is significantly less than the proportion of black respondents.