A researcher selects a sample of 100 participants from a population with a mean of 38 and a standard deviation of 20.About 68% of the sample means in this sampling distribution should be between a sample mean of
A) 18 and 58.
B) 34 and 38.
C) 38 and 44.
D) 36 and 40.

Question

Quizplus · Accepted Answer

We can use the Central Limit Theorem to determine the range of sample means:

mean of sampling distribution of x̄ = population mean = 38 
standard deviation of sampling distribution of x̄ = population standard deviation / sqrt(sample size) = 20 / sqrt(100) = 2

68% of sample means will fall within one standard deviation of the mean:

38 - 2 = 36 
38 + 2 = 40

Therefore, the range of sample means in which 68% of the sample means should fall is between 36 and 40. Thus, choice D is the correct answer.

A Researcher Selects a Sample of 100 Participants from a Population