Question

Suppose that a think tank is interested in voter participation. The conventional wisdom, based
on the 2012 congressional elections, is that 59 percent of eligible voters cast ballots in
congressional races. This think tank has conducted a major voter education campaign in a
district. To assess the impact of their campaign, they surveyed n = 846 eligible voters. Of those,
530 indicated they planned to vote in the upcoming election. Conduct the appropriate hypothesis
test to see whether or not the campaign had a meaningful effect (two-tailed test). In other words,
test the conventional wisdom against the hypothesis that it is not the parameter value. Use
significance level α = 0.05, and clearly state the hypotheses, the test statistic, the p-value, and
your conclusion.

Answer 1

Solution :

Given that ,

n =846

x = 530

The null and alternative hypothesis is ,

H₀ : p = 0.59

H_a : p 0.59

This is the two tailed test .

= x / n = 530 / 846 = 0.6265

P₀ = 59% = 0.59

1 - P₀ = 1 - 0.59 = 0.41

Test statistic = z

= - P₀ / [P_{0 *} (1 - P₀ ) / n]

= 0.6265 - 0.59 / [0.59 (1 - 0.59 ) / 846 ]

= 2.157

The test statistic = 2.157

P-value = 0.0310

= 0.05   

0.0310 < 0.05

P-value <

Reject the null hypothesis .

There is sufficient evidence to test the claim .