Reading 10: Sampling and Estimation - LOS e ～ Q1-5 standard, industry, management, class

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1.Melissa Cyprus, CFA, is conducting an analysis of inventory management practices in the retail industry. She assumes the population cross-sectional standard deviation of inventory turnover ratios is 20. How large a random sample should she gather in order to ensure a standard error of the sample mean of 4?

A)   20.

B)   25.

C)   5.

D)   80.

2.A population has a mean of 20,000 and a standard deviation of 1,000. Samples of size n = 2,500 are taken from this population. What is the standard error of the sample mean?

A)   0.04.

B)   400.00.

C)   20.00.

D)   8.00.

3.From a population of 5,000 observations, a sample of n = 100 is selected. Calculate the standard error of the sample mean if the population standard deviation is 50.

A)   4.48.

B)   5.00.

C)   4.00.

D)   50.00.

4.From a population with a known standard deviation of 15, a sample of 25 observations is taken. Calculate the standard error of the sample mean.

A)   1.67.

B)   3.00.

C)   0.60.

D)   15.00.

5.A sample of size n = 25 is selected from a normal population. This sample has a mean of 15 and a sample variance of 4. What is the standard error of the sample mean?

A)   2.0.

B)   0.4.

C)   0.8.

D)   1.0.

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答案和详解如下：

1.Melissa Cyprus, CFA, is conducting an analysis of inventory management practices in the retail industry. She assumes the population cross-sectional standard deviation of inventory turnover ratios is 20. How large a random sample should she gather in order to ensure a standard error of the sample mean of 4?

A)   20.

B)   25.

C)   5.

D)   80.

The correct answer was B)    

Given the population standard deviation and the standard error of the sample mean, you can solve for the sample size. Because the standard error of the sample mean equals the standard deviation of the population divided by the square root of the sample size, 4 = 20 / n^1/2, so n^1/2 = 5, so n = 25.

2.A population has a mean of 20,000 and a standard deviation of 1,000. Samples of size n = 2,500 are taken from this population. What is the standard error of the sample mean?

A)   0.04.

B)   400.00.

C)   20.00.

D)   8.00.

The correct answer was C)

The standard error of the sample mean is estimated by dividing the standard deviation of the sample by the square root of the sample size: s_x = s / n^1/2 = 1000 / (2500)^1/2 = 1000 / 50 = 20.

3.From a population of 5,000 observations, a sample of n = 100 is selected. Calculate the standard error of the sample mean if the population standard deviation is 50.

A)   4.48.

B)   5.00.

C)   4.00.

D)   50.00.

The correct answer was B)

The standard error of the sample mean equals the standard deviation of the population divided by the square root of the sample size: 50 / 100^1/2 = 5.

4.From a population with a known standard deviation of 15, a sample of 25 observations is taken. Calculate the standard error of the sample mean.

A)   1.67.

B)   3.00.

C)   0.60.

D)   15.00.

The correct answer was B)    

The standard error of the sample mean equals the standard deviation of the population divided by the square root of the sample size: s_x = s / n^1/2 = 15 / 25^1/2 = 3.

5.A sample of size n = 25 is selected from a normal population. This sample has a mean of 15 and a sample variance of 4. What is the standard error of the sample mean?

A)   2.0.

B)   0.4.

C)   0.8.

D)   1.0.

The correct answer was B)

The standard error of the sample mean is estimated by dividing the standard deviation of the sample by the square root of the sample size. The standard deviation of the sample is calculated by taking the positive square root of the sample variance 4^1/2 = 2. Applying the formula: s_x = s / n^1/2 = 2 / (25)^1/2 = 2 / 5 = 0.4.