Reading 11: Hypothesis Testing - LOS a, (Part 1) ～ Q11-13 class, black, style, critical

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11.The critical value is:

A)   -2.33.

B)   2.17.

C)   -2.38.

D)   2.47.

12.You should:

A)   accept the null hypothesis.

B)   reject the alternative hypothesis.

C)   reject the null hypothesis.

D)   Cannot be determined with the information given.

13.An analyst conducts a two-tailed test to determine if mean earnings estimates are significantly different from reported earnings. The sample size is greater than 25 and the computed test statistic is 1.25. Using a 5% significance level, which of the following statements is most accurate?

A)   The analyst should fail to reject the null hypothesis and conclude that the earnings estimates are not significantly different from reported earnings.

B)   The appropriate test to apply is a two-tailed chi-square test.

C)   To test the null hypothesis, the analyst must determine the exact sample size and calculate the degrees of freedom for the test.

D)   The analyst should reject the null hypothesis and conclude that the earnings estimates are significantly different from reported earnings.

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答案和详解如下：

11.The critical value is:

A)   -2.33.

B)   2.17.

C)   -2.38.

D)   2.47.

The correct answer was A)    

This is a one-tailed test with a significance level of 0.01. The critical value for a one-tailed test at a 1% level of significance is -2.33.

12.You should:

A)   accept the null hypothesis.

B)   reject the alternative hypothesis.

C)   reject the null hypothesis.

D)   Cannot be determined with the information given.

The correct answer was C)

The calculated test statistic of -4.24 falls to the left of the z-statistic of -2.33, and is in the rejection region. Thus, the null hypothesis is rejected and the conclusion is that the population mean is less than 133.

13.An analyst conducts a two-tailed test to determine if mean earnings estimates are significantly different from reported earnings. The sample size is greater than 25 and the computed test statistic is 1.25. Using a 5% significance level, which of the following statements is most accurate?

A)   The analyst should fail to reject the null hypothesis and conclude that the earnings estimates are not significantly different from reported earnings.

B)   The appropriate test to apply is a two-tailed chi-square test.

C)   To test the null hypothesis, the analyst must determine the exact sample size and calculate the degrees of freedom for the test.

D)   The analyst should reject the null hypothesis and conclude that the earnings estimates are significantly different from reported earnings.

The correct answer was A)

The null hypothesis is that earnings estimates are equal to reported earnings. To reject the null hypothesis, the calculated test statistic must fall outside the two critical values. IF the analyst tests the null hypothesis with a z-statistic, the crtical values at a 5% confidence level are +/-1.96. Because the calculated test statistic, 1.25, lies between the two critical values, the analyst should fail to reject the null hypothesis and conclude that earnings estimates are not significantly different from reported earnings. If the analyst uses a t-statistic, the upper critical value will be even greater than 1.96, never less, so even without the exact degrees of freedom the analyst knows any t-test would fail to reject the null.