Question

A researcher looks at a large set of data and concludes the population has a standard deviation of 40. Using sample sizes of 64, the researcher is able to focus the mean of the means of the sample to a narrower distribution where the standard deviation is 5. Then, the researcher realizes there was an error in the original calculations, and the initial standard deviation is really 20. What is the correct value of the standard deviation of the means of the samples?

a) 2.5
b) 5
c) 10
d) 20

Answer 1

The correct value of the standard deviation of the means of the samples is 2.5. Therefore, the correct value of the standard deviation of the means of the samples is 2.5 (a).

Step-by-step explanation:

The correct value of the standard deviation of the means of the samples can be calculated using the formula:

Correct standard deviation = Initial standard deviation / √sample size

In this case, the initial standard deviation is 20 and the sample size is 64, so the correct standard deviation of the means of the samples is:

Correct standard deviation = 20 / √64 = 20 / 8 = 2.5

Therefore, the correct value of the standard deviation of the means of the samples is 2.5 (a).