Reading 11: Hypothesis Testing - LOS b, (Part 1) ～ Q1-4

答案和详解如下：

1.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)   1.78.

C)   -19.06.

D)   -1.78.

The correct answer was 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

2.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)   19.99.

B)   2.31.

C)   -19.99.

D)   -2.31.

The correct answer was A)

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.

3.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)   -21.62.

D)   -1.63.

The correct answer was 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.”

4.A survey is taken to determine whether the average starting salaries of CFA charterholders is equal to or greater than $59,000 per year. What is the test statistic given a sample of 135 newly acquired CFA charterholders with a mean starting salary of $64,000 and a standard deviation of $5,500?

A)   0.91.

B)   -10.56.

C)   -0.91.

D)   10.56.

The correct answer was D)

With a large sample size (135) 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) = (64,000 – 59,000) / (5,500 / 135^1/2) = (5,000) / (5,500 / 11.62) = 10.56.