Exhibit 9-1

Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

Question

Exhibit 9-1

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Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

BlackTom AI · Accepted Answer

To analyze this hypothesis test, I will first lay out the given data and hypotheses, then compute the test statistic and compare it to the critical value at the specified significance level.

Option A: 'Not enough information is given to answer this question.' The problem provides n, x-bar, sigma, and the hypotheses, as well as the significance level. Therefore, there is enough information to perform the z-test and decide whether to reject H0. This statement is incorrect.

Option B: 'be tested again.' This would imply that the data are insufficient or something is missing to perform the test, which is not the case here. We have all necessary components (sample size, sample mean, population sigma, and hypotheses). This option is incorrect.

Option C: 'not be rejected.' This aligns with the computation: compute the z-statistic z = (xbar - mu0) / (sigma / sqrt(n)) = (24.6 - 20) / (12 / sqrt(36)) = 4.6 / 2 = 2.3. The one-sided test at alpha = 0.01 has a critical z value around 2.326. Since 2.3 is less than 2.326, the observed statistic does not exceed the critical value, so we fail to reject H0. Therefore, this option is correct.

Option D: 'be rejected.' This would require the test statistic to exceed the critical value of about 2.326 in the positive tail for a one-sided test at 0.01. Since 2.3 < 2.326, we do not reject H0. Thus this statement is incorrect.

In summary, by comparing the calculated z = 2.3 to the critical value 2.326 at alpha = 0.01 for a right-tailed test, the result is fail to reject the null hypothesis. The only option that matches this conclusion is 'not be rejected.'

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Exhibit 9-1 Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.

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Exhibit 9-1 ​ ​ Refer to Exhibit 9-1. If the test is done at a .01 level of significance, the null hypothesis should _____.