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Question
Math
Posted 3 months ago

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%45 \% of voters, so the manager wants to test H0:p=0.45H_{0}: p=0.45 versus Ha:p<0.45H_{\mathrm{a}}: p<0.45, where pp 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 z0.45z \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 α=0.05\alpha=0.05 significance level?

Choose 1 answer:
(A) They can conclude that less than 45%45 \% of voters support the opposing candidate.
(B) They can conclude that more than 45%45 \% of voters support the opposing candidate.
C) They cannot conclude that less than 45%45 \% of voters support the opposing candidate.

D They can conclude that exactly 45%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 α\alpha
step 3
Draw a conclusion based on the comparison between the P-value and α\alpha
1 Answer
C) They cannot conclude that less than 45%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 α\alpha, we fail to reject the null hypothesis. Since the P-value of 0.33 is greater than α=0.05\alpha = 0.05, we cannot conclude that less than 45%45\% of voters support the opposing candidate.

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