Question

Math

Posted 3 months ago

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A campaign manager for a political candidate released a series of advertisements criticizing the opposing candidate in an upcoming election. The opposing candidate previously had the support of $45 \%$ of voters, so the manager wants to test $H_{0}: p=0.45$ versus $H_{\mathrm{a}}: p<0.45$, where $p$ is the proportion of voters that support the opposing candidate.
After running the advertisements, the campaign manager obtained a random sample of 500 voters and found that 220 of those sampled supported the opposing candidate. The resulting test statistic was $z \approx-0.45$ and the P-value was approximately 0.33 .
Assuming the conditions for inference were met, what is an appropriate conclusion at the $\alpha=0.05$ significance level?
Choose 1 answer:
(A) They can conclude that less than $45 \%$ of voters support the opposing candidate.
(B) They can conclude that more than $45 \%$ of voters support the opposing candidate.
C) They cannot conclude that less than $45 \%$ of voters support the opposing candidate.
D They can conclude that exactly $45 \%$ of voters support the opposing candidate.
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Answer from Sia

Posted 3 months ago

Solution by Steps

step 1

Determine the significance level for the hypothesis test

step 2

Compare the P-value to the significance level $\alpha$

step 3

Draw a conclusion based on the comparison between the P-value and $\alpha$

1 Answer

C) They cannot conclude that less than $45\%$ of voters support the opposing candidate.

Key Concept

Hypothesis Testing and P-value Interpretation

Explanation

In hypothesis testing, if the P-value is greater than the significance level $\alpha$, we fail to reject the null hypothesis. Since the P-value of 0.33 is greater than $\alpha = 0.05$, we cannot conclude that less than $45\%$ of voters support the opposing candidate.

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