can we reject the null hypothesis?

Question

You would like to know if people give different responses to white interviewers than to nonwhite interviewers. To explore this, you use the American National Election Studies 2008 data in order to cross tabulate interviewer race with a survey question that asks whether the respondent thinks the “US is ready for an African-American President.” 1227 of the 1942 respondents (63%) interviewed by a white interviewer answered in the affirmative; 165 of the 230 respondents (72%) interviewed by a nonwhite interviewer answered in the affirmative.

 

(1a) Given these data and an alpha level of .05, can you reject the null hypothesis that interviewer race and respondent attitudes are independent? Why or why not?

Answer 1

State the hypotheses. The first step is to state the null hypothesis and an alternative hypothesis.

Null hypothesis H0: P1 = P2
Alternative hypothesis H1: P1 ≠ P2

Note that these hypotheses constitute a two-tailed test. The null hypothesis will be rejected if the proportion from population 1 is too big or if it is too small.

Formulate an analysis plan. For this analysis, the significance level is 0.05. The test method is a two-proportion z-test.

Analyze sample data. Using sample data, we calculate the pooled sample proportion (p) and the standard error (SE). Using those measures, we compute the z-score test statistic (z).

p1=.63 and n1=1942

p2=.72 and n2=230
p = (p1 * n1 + p2 * n2) / (n1 + n2)=......

 

SE = sqrt{ p * ( 1 - p ) * [ (1/n1) + (1/n2) ] }=.......

 

z = (p1 - p2) / SE =.......  This is calculated z test value (Z_calculated)

 

The p-value or critical value at 0.05 level of significance for two tail test is Z_critical(which is given value from z table)

 

Conclusion: Z_calculated > Z_critical then we reject Null hypothesis that interviewer race and respondent attitudes are independent