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Reading 11: Hypothesis Testing - LOS a, (Part 1) ~ Q1-5

1.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)   To test the claim that X is greater than zero, the null hypothesis would be H0: X>0.

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

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

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

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

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

3.Which of the following statements least describes the procedure for testing a hypothesis?

A)   Compute the sample value of the test statistic, set up a rejection (critical) region, and make a decision.

B)   Develop a hypothesis, compute the test statistic, and make a decision.

C)   Select the level of significance, formulate the decision rule, and make a decision.

D)   Select the level of significance, compute the test statistic, and make a decision.

4.The first step in the process of hypothesis testing is:

A)   the collection of the sample.

B)   to state the hypotheses.

C)   the calculation of sample statistics.

D)   selecting the test statistic.

5.In the process of hypothesis testing, what is the proper order for these steps?

A)   Specify the level of significance. State the hypotheses. Make a decision. Collect the sample and calculate the sample statistics.

B)   State the hypotheses. Collect the sample and calculate the sample statistics. Make a decision. Specify the level of significance.

C)   Collect the sample and calculate the sample statistics. State the hypotheses. Specify the level of significance. Make a decision.

D)   State the hypotheses. Specify the level of significance. Collect the sample and calculate the test statistics. Make a decision.

答案和详解如下:

1.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)   To test the claim that X is greater than zero, the null hypothesis would be H0: X>0.

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

The correct answer was 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. The appropriate null would be "X ≤ 0" with "X > 0" as the alternative hypothesis.

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

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

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

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

The correct answer was 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.

3.Which of the following statements least describes the procedure for testing a hypothesis?

A)   Compute the sample value of the test statistic, set up a rejection (critical) region, and make a decision.

B)   Develop a hypothesis, compute the test statistic, and make a decision.

C)   Select the level of significance, formulate the decision rule, and make a decision.

D)   Select the level of significance, compute the test statistic, and make a decision.

The correct answer was A)

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.

4.The first step in the process of hypothesis testing is:

A)   the collection of the sample.

B)   to state the hypotheses.

C)   the calculation of sample statistics.

D)   selecting the test statistic.

The correct answer was B)

The researcher must state the hypotheses prior to the collection and analysis of the data. More importantly, it is necessary to know the hypotheses before selecting the appropriate test statistic.

5.In the process of hypothesis testing, what is the proper order for these steps?

A)   Specify the level of significance. State the hypotheses. Make a decision. Collect the sample and calculate the sample statistics.

B)   State the hypotheses. Collect the sample and calculate the sample statistics. Make a decision. Specify the level of significance.

C)   Collect the sample and calculate the sample statistics. State the hypotheses. Specify the level of significance. Make a decision.

D)   State the hypotheses. Specify the level of significance. Collect the sample and calculate the test statistics. Make a decision.

The correct answer was D)

The hypotheses must be established first. Then the test statistic is chosen and the level of significance is determined. Following these steps, the sample is collected, the test statistic is calculated, and the decision is made.

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