Question

After the political ad​ campaign, pollsters check the prime minister​'s negatives. They test the hypothesis that the ads produced no change against the alternative that the negatives are now below 54​% and find a​ P-value of 0.089. Which conclusion is​ appropriate? Explain.
Choose the correct answer below.
There is a 8.9​% chance that natural sampling variation could produce poll results at least as far below 54​% as these if there is really no change in public opinion.
B.
There is a 8.9​% chance that the poll they conducted is correct.
C.
There is a 8.9​% chance that the ads worked.
D.
There is a 91.1​% chance that the ads worked.

Answer 1

The given problem is about the study of the negatives after the political ad campaign. Under this

study, the null and alternative hypotheses are

$H_0:p=0.54$

$H_1:p<0.54$

The sample test results yield the P-value is 0.089.

The P-value is is the probability, calculated assuming that the null hypothesis is true, of obtaining a value of the test statistic at least as contradictory to $H_0$ as the value calculated from the available sample.

Select a significance level $\alpha=0.05.$

$p=0.089>0.05=\alpha.$

The correct option is

A. There is a 8.9​% chance that natural sampling variation could produce poll results at least as far below 54​% as these if there is really no change in public opinion.