Question

Suppose that a survey of 500 randomly selected registered voters are asked whether they voted in

the last presidential election and that 49% said that they had. We wish to test the claim at the a = 0.05 level of

significance that more than 50% of registered voters voted in the last presidential election.

Answer 1

Null hypothesis: $H_0:p=0.5$

Alternative hypothesis: $H_a:p>0.5$

The test statistic is found using n=500 and $\^p=0.49$ . We get

$z=\frac{0.49-0.5}{\sqrt{\frac{0.5*0.5}{500}}}=-0.4472.$

At $\alpha=0.05$ the critical value $z$ will be $z=1.645$ (using t-table).

The rejection region for this right-tailed test is $R = \{z: z > 1.645\}.$

Our test statistic does not fall within the rejection region (it is less than 1.645), so we cannot reject the null hypothesis.