Question

A survey by Pew in 2011 found that 56% of Americans believe that “The Civil War is still relevant to American politics and public life today” (http://people-press.org/2011/04/08/civil-war-at-150-still-relevant-still-divisive/). We hypothesize that the percentage of people who believe the Civil War is still relevant will be higher in Southern states (like GA) than in the US as a whole.

Let’s say we conduct our own survey of Georgians to test this hypothesis and find, based on a survey of 30 Georgians, that the percentage of people believing the war is still relevant is 58% (SD=5%). Relying on the t-distribution chart, please determine whether the null hypothesis can be rejected in this case (at a p<.01 level of significance) and interpret the results.

Answer 1

p = 0.56

n = 30, = 0.58, = 0.01

The Hypothesis:

H0: p = 0.56

Ha: p > 0.56

The Test Statistic:

The p Value:    The p value (right tail tail) for t = 0.22, df = n - 1 = 29 is; p value = 0.4137

The Decision: Since p value > 0.01, we fail to reject H0.

The Conclusion:   There is not sufficient evidence at the 99% significance level to conclude that the percentage of people who believe that war is still relevant is greater than 56%.