Q13. A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $58,500 per year. What is the test statistic given a sample of 175 newly acquired CFA charterholders with a mean starting salary of $67,000 and a standard deviation of $5,200?

A)      21.62.

B)      -1.63.

C)      1.63.

Q14. A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $54,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 75 newly acquired CFA charterholders with a mean starting salary of $57,000 and a standard deviation of $1,300?

A)   2.31.

B)   -19.99.

C)   19.99.

Q15. A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $57,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 115 newly acquired CFA charterholders with a mean starting salary of $65,000 and a standard deviation of $4,500?

A)   19.06.

B)   -19.06.

C)   1.78.

Q16. If a two-tailed hypothesis test has a 5% probability of rejecting the null hypothesis when the null is true, it is most likely that the:

A)   probability of a Type I error is 2.5%.

B)   power of the test is 95%.

C)   significance level of the test is 5%.

Q17. Which of the following statements about hypothesis testing is most accurate? A Type II error is the probability of:

A)   failing to reject a false null hypothesis.

B)   rejecting a true alternative hypothesis.

C)   rejecting a true null hypothesis.

答案和详解如下：

Q13. A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $58,500 per year. What is the test statistic given a sample of 175 newly acquired CFA charterholders with a mean starting salary of $67,000 and a standard deviation of $5,200?

A)      21.62.

B)      -1.63.

C)      1.63.

Correct answer is A)

With a large sample size (175) the z-statistic is used. The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) / (population standard deviation / (sample size)^1/2 = (X − µ) / (σ / n^1/2) = (67,000 – 58,500) / (5,200 / 175^1/2) = (8,500) / (5,200 / 13.22) = 21.62.

Q14. A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $54,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 75 newly acquired CFA charterholders with a mean starting salary of $57,000 and a standard deviation of $1,300?

A)   2.31.

B)   -19.99.

C)   19.99.

Correct answer is C)

With a large sample size (75) the z-statistic is used. The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) / (population standard deviation / (sample size)^1/2 = (X − µ) / (σ / n^1/2) = (57,000 – 54,000) / (1,300 / 75^1/2) = (3,000) / (1,300 / 8.66) = 19.99.

Q15. A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $57,000 per year. Assuming a normal distribution, what is the test statistic given a sample of 115 newly acquired CFA charterholders with a mean starting salary of $65,000 and a standard deviation of $4,500?

A)   19.06.

B)   -19.06.

C)   1.78.

Correct answer is A)

With a large sample size (115) the z-statistic is used. The z-statistic is calculated by subtracting the hypothesized parameter from the parameter that has been estimated and dividing the difference by the standard error of the sample statistic. Here, the test statistic = (sample mean – hypothesized mean) / (population standard deviation / (sample size)^1/2 = (X − µ) / (σ / n^1/2) = (65,000 – 57,000) / (4,500 / 115^1/2) = (8,000) / (4,500 / 10.72) = 19.06.

Q16. If a two-tailed hypothesis test has a 5% probability of rejecting the null hypothesis when the null is true, it is most likely that the:

A)   probability of a Type I error is 2.5%.

B)   power of the test is 95%.

C)   significance level of the test is 5%.

Correct answer is C)

Rejecting the null hypothesis when it is true is a Type I error. The probability of a Type I error is the significance level of the test. The power of a test is one minus the probability of a Type II error, which cannot be calculated from the information given.

Q17. Which of the following statements about hypothesis testing is most accurate? A Type II error is the probability of:

A)   failing to reject a false null hypothesis.

B)   rejecting a true alternative hypothesis.

C)   rejecting a true null hypothesis.

Correct answer is A)

The Type II error is the error of failing to reject a null hypothesis that is not true.

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