1、A securities analyst is performing a hypothesis test on the average earnings per share for a sample of large-cap companies. The sample size is large and the population variance is known. The development of a 95 percent confidence interval around the average EPS value requires all of the following EXCEPT a:

A)   sample average EPS.

B)   population standard deviation divided by the square root of the sample size.

C)   Critical one-sided t-value with .05 in the right tail.

D)   Z-score of 1.96.

2、Construct a 90 percent confidence interval for the starting salaries of 100 recently hired employees with average starting salaries of $50,000 and a standard deviation of $3,000 assuming the population has a normal distribution.

A)   50000 +/- 1.65(3000).

B)   50000 +/- 1.65(300).

C)   30000 +/- 1.65(5000).

D)   50000 +/- 1.65(30000).

3、For a normal distribution, what approximate percentage of the observations fall within ±3 standard deviation of the mean?

A)   95%.

B)   66%.

C)   99%.

D)   50%.

4、A stock portfolio's returns are normally distributed. It has had an average annual return of 25 percent. The 90 percent confidence interval for the returns is –41 to 91 percent. What is the 99 percent confidence interval?

A)   -78.2 to 128.2%.

B)   -66 to 116%.

C)   -58.4 to 98.4%.

D)   -20 to 20%.

5、A stock portfolio has had a historical average annual return of 12 percent and a standard deviation of 20 percent. The returns are normally distributed. The range –27.2 to 51.2 percent describes a:

A)   95% confidence interval.

B)   68% confidence interval.

C)   50% confidence interval.

D)   99% confidence interval.

6、The mean return of a portfolio is 20% and its standard deviation is 4%. The returns are normally distributed. Which of the following statements about this distribution are least accurate? The probability of receiving a return:

A)   of less than 12% is 0.025.

B)   between 12% and 28% is 0.95.

C)   in excess of 16% is 0.16.

D)   between 16% and 28% is 0.815.

答案和详解如下：

1、A securities analyst is performing a hypothesis test on the average earnings per share for a sample of large-cap companies. The sample size is large and the population variance is known. The development of a 95 percent confidence interval around the average EPS value requires all of the following EXCEPT a:

A)   sample average EPS.

B)   population standard deviation divided by the square root of the sample size.

C)   Critical one-sided t-value with .05 in the right tail.

D)   Z-score of 1.96.

The correct answer was C)

Since the sample size is large and the population variance is known, we use the two-tailed Z-score of 1.96 (2.5% in each tail) and the standard error computed using population standard deviation. The confidence interval is Sample Average EPS +/- 1.96(Standard Error).

2、Construct a 90 percent confidence interval for the starting salaries of 100 recently hired employees with average starting salaries of $50,000 and a standard deviation of $3,000 assuming the population has a normal distribution.

A)   50000 +/- 1.65(3000).

B)   50000 +/- 1.65(300).

C)   30000 +/- 1.65(5000).

D)   50000 +/- 1.65(30000).

The correct answer was A)    

90% confidence interval is X ± 1.65s = 50000 ± 1.65(3000) = $45,050 to $54,950

3、For a normal distribution, what approximate percentage of the observations fall within ±3 standard deviation of the mean?

A)   95%.

B)   66%.

C)   99%.

D)   50%.

The correct answer was C)    

For normal distributions, approximately 99% of the observations fall within ±3 standard deviations of the mean.

4、A stock portfolio's returns are normally distributed. It has had an average annual return of 25 percent. The 90 percent confidence interval for the returns is –41 to 91 percent. What is the 99 percent confidence interval?

A)   -78.2 to 128.2%.

B)   -66 to 116%.

C)   -58.4 to 98.4%.

D)   -20 to 20%.

The correct answer was A)

A 90 percent confidence level includes the range between plus and minus 1.65 standard deviations from the mean. Dividing the size of this range by 1.65 gives the size of one standard deviation: (91 - 25) / 1.65 = 40. A 99 percent confidence level includes the range between plus and minus 2.58 standard deviations from the mean. Multiplying the standard deviation of 40 by 2.58 and then adding and subtracting the result from the mean produces the 99 percent confidence interval: (25 – (2.58 * 40) = -78.20 is the lower end of the range, and (25 + (2.58 * 40) = 128.20 is the higher end of the range.

5、A stock portfolio has had a historical average annual return of 12 percent and a standard deviation of 20 percent. The returns are normally distributed. The range –27.2 to 51.2 percent describes a:

A)   95% confidence interval.

B)   68% confidence interval.

C)   50% confidence interval.

D)   99% confidence interval.

The correct answer was A)

The upper limit of the range, 51.2 percent, is (51.2 – 12) = 39.2 / 20 = 1.96 standard deviations above the mean of 12. The lower limit of the range is (12 – (-27.2)) = 39.2 / 20 = 1.96 standard deviations below the mean of 12. A 95 percent confidence level is defined by a range 1.96 standard deviations above and below the mean.

6、The mean return of a portfolio is 20% and its standard deviation is 4%. The returns are normally distributed. Which of the following statements about this distribution are least accurate? The probability of receiving a return:

A)   of less than 12% is 0.025.

B)   between 12% and 28% is 0.95.

C)   in excess of 16% is 0.16.

D)   between 16% and 28% is 0.815.

The correct answer was C)    

The probability of receiving a return greater than 16% is calculated by adding the probability of a return between 16% and 20% (given a mean of 20% and a standard deviation of 4%, this interval is the left tail of one standard deviation from the mean, which includes 34% of the observations.) to the area from 20% and higher (which starts at the mean and increases to infinity and includes 50% of the observations.) The probability of a return greater than 16% is 34 + 50 = 84%.

Note: 0.16 is the probability of receiving a return less than 16%.