An SRS of 45 male employees at a large company found that 36 felt that the company was supportive of female employees. An independent SRS of 40 female employees found that 24 felt that the company was supportive of female employees. Let p1 = the proportion of all male employees at the company and p2 = the proportion of all female employees at the company who hold this opinion. We want to test the hypotheses, . The P-value for this test is 0.0217. Which of the following is the correct conclusion using a = 0.01?

Question

An SRS of 45 male employees at a large company found that 36 felt that the company was supportive of female employees. An independent SRS of 40 female employees found that 24 felt that the company was supportive of female employees. Let p1 = the proportion of all male employees at the company and p2 = the proportion of all female employees at the company who hold this opinion.  We want to test the hypotheses, .  The P-value for this test is 0.0217.  Which of the following is the correct conclusion using a = 0.01?

BlackTom AI · Accepted Answer

We start by identifying the hypotheses and the given P-value and significance level.
- The test is a one-sided test comparing p1 to p2, with Ha likely being p1 > p2 (since the question mentions testing whether the proportion of male employees who feel the company is supportive of female employees is higher).
- The given P-value for this test is 0.0217, and the significance level alpha (a) is 0.01.

Option A: 'Accept Ha. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way.'
- In hypothesis testing, we never literally 
  accept Ha; we either reject H0, or fail to reject H0. The wording here uses 'Accept Ha', which is not standard practice and misleading. Also, the P-value being 0.0217 means we do not have strong evidence at alpha = 0.01 to conclude Ha; this option’s terminology and conclusion are therefore inappropriate and incorrect.

Option B: 'Fail to reject H0. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way.'
- This aligns with the standard procedure: since P = 0.0217 is greater than alpha = 0.01, we do not reject H0 at the 1% significance level. The statement correctly reflects that we lack convincing evidence to support Ha at this level. The conclusion uses the conventional phrasing 'fail to reject H0,' which is appropriate.

Option C: 'Accept H0. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way.'
- Similar to Option A, the word 'Accept H0' is not the standard terminology in hypothesis testing. We typically say 'fail to reject H0' rather than 'accept H0.' While the substantive conclusion about evidence is aligned, the phrasing is not correct in standard statistical practice, making this option incorrect.

Option D: 'Reject H0. We do not have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way.'
- If we reject H0, we would have evidence in favor of Ha, not against it. This option contains a contradictory combination: it asserts rejecting H0 while also stating there is no convincing evidence for Ha. Given P = 0.0217 and alpha = 0.01, we do not reject H0, so this option is inconsistent with the data and was therefore incorrect.

Option E: 'Reject H0. We have convincing evidence that the proportion of male employees who feel that the company is supportive of female employees is higher than the proportion of women who feel this way.'
- This would require P ≤ alpha to claim convincing evidence, and with alpha = 0.01 the P-value 0.0217 does not meet this threshold. Additionally, the result would imply Ha is true, which is not supported at the 1% level. Therefore, this option is incorrect.

In summary, evaluating the standard testing framework and the given P-value against the 0.01 significance level, only Option B uses the correct testing language and matches the decision rule for this P-value. The other options either misuse terminology (Accept/Reject Ha vs fail to reject H0), mix up the direction of evidence, or contradict the standard interpretation of a P-value relative to alpha.

AP Statistics-Deputron-T2-2025 Trimester 2 Final Exam MC Review #2

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