Question

Given a population mean of 53.7 with a standard deviation of 1.3 and a sample size

of 6, answer these questions:

Part A: What is the standard deviation of the sampling distribution of X? Show your

work. (5 points)

Part B: What does the sample size need to be if you want the standard deviation of

the sampling distribution of x to be 0.325? Show your work. (5 points) (10 points)

Answer 1

The standard deviation of the sampling distribution of X can be found by dividing the population standard deviation by the square root of the sample size. To find the sample size needed for a specific standard deviation, we can rearrange the formula. In this case, the sample size needed is 16.

Step-by-step explanation:

Part A:

The standard deviation of the sampling distribution of X is the population standard deviation (1.3) divided by the square root of the sample size (6).

Therefore, the standard deviation of the sampling distribution of X is 1.3 / sqrt(6) = 0.53.

Part B:

To find the sample size needed to have a standard deviation of 0.325 for the sampling distribution of X, we can rearrange the formula from Part A.

0.325 = 1.3 / sqrt(n)

sqrt(n) = 1.3 / 0.325

sqrt(n) = 4

n = 16

Therefore, the sample size needed is 16.