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

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

leiyou

 

The correct answer is C

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.

leiyou

 

AIM 11: Define and interpret the null hypothesis, the alternative hypothesis.

1、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) A sample size of 200 indicates that we should fail to reject the null.

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

D) 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%.

leiyou

 

The 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 HA: 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%.

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3、Which of the following statements about hypothesis testing is most accurate?

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

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

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

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

leiyou

 

The correct answer is D

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.

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4、Which of the following statements least describes the procedure for testing a hypothesis?

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

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

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

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

leiyou

 

The correct answer is D

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

Stating the hypotheses.

Identifying the test statistic and its probability distribution.

Specifying the significance level.

Stating the decision rule.

Collecting the data and performing the calculations.

Making the statistical decision.

Making the economic or investment decision.

leiyou

 

2、Which of the following statements about hypothesis testing is most accurate?

A) A hypothesized mean of 3, a sample mean of 6, and a standard error of the sampling means of 2 give a sample Z-statistic of 1.5.

B) A Type I error is rejecting the null hypothesis when it is true, and a Type II error is accepting the alternative hypothesis when it is false.

C) When the critical Z-statistic is greater than the sample Z-statistic in a two-tailed test, reject the null hypothesis and accept the alternative hypothesis.

D) A two-tailed test on a large sample with a significance level of 0.01 has confidence intervals of ±1.96 standard errors.

leiyou

 

The correct answer is A

The 0.01 level of significance has confidence intervals of ± 2.58 standard errors. A Type II error is wrongly accepting the null hypothesis. The null hypothesis should be rejected when the sample Z-statistic is greater than the critical Z-statistic.