leiyou

 

8、A random sample of 100 technology stocks earned an average of 10%. Assuming the distribution of equity returns is normal and the population standard deviation is 5%, the 95% confidence interval for the population mean is:

A) 5.00% to 15.00%.

B) 9.02% to 10.98%.

C) 9.50% to 10.50%.

D) 9.91% to 10.90%.

leiyou

 

The correct answer is B

Zα / 2 = Z0.025 = 1.96. So, 0.1 +/?1.96(0.05 / 10) = 9.02% to 10.98%.

leiyou

 

AIM 10: Explain the process of hypothesis testing.

1、Which of the following statements about testing a hypothesis using a Z-test is least accurate?

A) A Type I error is rejecting the null hypothesis when it is actually true.

B) The calculated Z-statistic determines the appropriate significance level to use.

C) If the calculated Z-statistic lies outside the critical Z-statistic range, the null hypothesis can be rejected.

D) The confidence interval for a two-tailed test of a population mean at the 5% level of significance is that the sample mean falls between ±1.96 σ/√n of the null hypothesis value.

leiyou

 

The correct answer is B

The significance level is chosen before the test so the calculated Z-statistic can be compared to an appropriate critical value.

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.

leiyou

 

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.

leiyou

 

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.