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

Q: 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 $\mathrm{P}$-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.

∻Solution by Steps∻ ‖ step 1 ⋮ Determine the significance level for the hypothesis test. ‖ ‖ step 2 ⋮ Compare the p-value to the significance level. ‖ ‖ step 3 ⋮ Draw a conclusion based on the comparison. ‖ ***C*** ∻Key Concept∻ ⚹Hypothesis Testing and P-value Interpretation⚹ ∻Explanation∻ ⚹If the p-value is greater than the significance level, we fail to reject the null hypothesis. In this case, with a p-value of 0.33 and a significance level of 0.05, we cannot conclude that less than 45% of voters support the opposing candidate.⚹◊What is the formula to calculate the test statistic (z-score) in hypothesis testing?⍭ Generate me a similar question◊

Question

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 $\mathrm{P}$-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.

Accepted Answer

∻Solution by Steps∻ ‖ step 1 ⋮ Determine the significance level for the hypothesis test. ‖ ‖ step 2 ⋮ Compare the p-value to the significance level. ‖ ‖ step 3 ⋮ Draw a conclusion based on the comparison. ‖ ***C*** ∻Key Concept∻ ⚹Hypothesis Testing and P-value Interpretation⚹ ∻Explanation∻ ⚹If the p-value is greater than the significance level, we fail to reject the null hypothesis. In this case, with a p-value of 0.33 and a significance level of 0.05, we cannot conclude that less than 45% of voters support the opposing candidate.⚹◊What is the formula to calculate the test statistic (z-score) in hypothesis testing?⍭ Generate me a similar question◊

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