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

 

6、What is the appropriate test statistic for constructing confidence intervals for the population mean of a nonnormal distribution when the population variance is unknown and the sample size is large (n ≥ 30)?

A) The z-statistic at α with n degrees of freedom.

B) The t-statistic at α with 29 degrees of freedom.

C) The z-statistic or the t-statistic.

D) The t-statistic at α/2 with n degrees of freedom.

leiyou

 

The correct answer is C

When the sample size is large, and the central limit theorem can be relied upon to assure a sampling distribution that is normal, either the t-statistic or the z-statistic is acceptable for constructing confidence intervals for the population mean. However, the t-statistic will provide a more conservative range (wider) at a given level of significance.

leiyou

 

7、The 95 percent confidence interval of the sample mean of the price earnings ratio for all traded stocks is 19 to 44. There are over 5,000 traded stocks and the sample size of this test is 100. Given that the expected value of the price earnings ratio is 31.5, the standard error of the ratio is closest to:

A) 1.96.

B) 2.58.

C) 12.50.

D) 6.38.

leiyou

 

The correct answer is

The confidence interval is 31.5 ± 1.96x, where x is the standard error. If we take the upper bound, we know that 31.5 +/– 1.96x = 44, or 1.96x = 12.5. Hence, x = 6.38.

leiyou

 

5、What is the appropriate test statistic for constructing confidence intervals for the population mean of a normal distribution when the population variance is unknown?

A) The t-statistic at α/2 with n degrees of freedom.

B) The z-statistic with n – 1 degrees of freedom.

C) The z-statistic at α with n degrees of freedom.

D) The t-statistic at α/2 with n – 1 degrees of freedom.

leiyou

 

The correct answer is D

Use the t-statistic at α/2 and n – 1 degrees of freedom when the population variance is unknown, regardless of sample size.