Q6. Which of the following is the correct sequence of events for testing a hypothesis?

A)   State the hypothesis, select the level of significance, compute the test statistic, formulate the decision rule, and make a decision.

B)   State the hypothesis, formulate the decision rule, select the level of significance, compute the test statistic, and make a decision.

C)   State the hypothesis, select the level of significance, formulate the decision rule, compute the test statistic, and make a decision.

Q7. Which of the following statements about hypothesis testing is most accurate?

A)   The probability of a Type I error is equal to the significance level of the test.

B)   If you can disprove the null hypothesis, then you have proven the alternative hypothesis.

C)   The power of a test is one minus the probability of a Type I error.

Q8. An analyst conducts a two-tailed z-test to determine if small cap returns are significantly different from 10%. The sample size was 200. The computed z-statistic is 2.3. Using a 5% level of significance, which statement is most accurate?

A)   You cannot determine what to do with the information given.

B)   Fail to reject the null hypothesis and conclude that small cap returns are close enough to 10% that we cannot say they are significantly different from 10%.

C)   Reject the null hypothesis and conclude that small cap returns are significantly different from 10%.

Q9. 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 reject the null hypothesis and conclude that the earnings estimates are significantly different from reported earnings.

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

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

答案和详解如下：

Q6. Which of the following is the correct sequence of events for testing a hypothesis?

A)   State the hypothesis, select the level of significance, compute the test statistic, formulate the decision rule, and make a decision.

B)   State the hypothesis, formulate the decision rule, select the level of significance, compute the test statistic, and make a decision.

C)   State the hypothesis, select the level of significance, formulate the decision rule, compute the test statistic, and make a decision.

Correct answer is C)

Depending upon the author there can be as many as seven steps in hypothesis testing which are:

1.      Stating the hypotheses.

2.      Identifying the test statistic and its probability distribution.

3.      Specifying the significance level.

4.      Stating the decision rule.

5.      Collecting the data and performing the calculations.

6.      Making the statistical decision.

7.      Making the economic or investment decision.

Q7. Which of the following statements about hypothesis testing is most accurate?

A)   The probability of a Type I error is equal to the significance level of the test.

B)   If you can disprove the null hypothesis, then you have proven the alternative hypothesis.

C)   The power of a test is one minus the probability of a Type I error.

Correct answer is A)

The probability of getting a test statistic outside the critical value(s) when the null is ture is the level of significance and is the probability of a Type I error. The power of a test is 1 minus the probability of a Type II error. Hypothesis testing does not prove a hypothesis, we either reject the null or fail to reject it.

Q8. An analyst conducts a two-tailed z-test to determine if small cap returns are significantly different from 10%. The sample size was 200. The computed z-statistic is 2.3. Using a 5% level of significance, which statement is most accurate?

A)   You cannot determine what to do with the information given.

B)   Fail to reject the null hypothesis and conclude that small cap returns are close enough to 10% that we cannot say they are significantly different from 10%.

C)   Reject the null hypothesis and conclude that small cap returns are significantly different from 10%.

Correct answer is C)

At the 5% level of significance the critical z-statistic for a two-tailed test is 1.96 (assuming a large sample size). The null hypothesis is H₀: x = 10%. The alternative hypothesis is H_A: x ≠ 10%. Because the computed z-statistic is greater than the critical z-statistic (2.33 > 1.96), we reject the null hypothesis and we conclude that small cap returns are significantly different than 10%.

Q9. 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 reject the null hypothesis and conclude that the earnings estimates are significantly different from reported earnings.

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

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

Correct answer is B)

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.