Question

A random sample of size 36 is taken from a population with mean µ = 18 and standard deviation σ = 5. What are the expected value and the standard deviation for the sampling distribution of the sample mean? Group of answer choices a. 1.425 and 2.66, respectively b. 18 and 5, respectively c. 1.425 and 0.83, respectively d. 18 and 0.83, respectively

Answer 1

Solution:

Given in the question

Population mean = 18

Population standard deviation = 5

No. Of sample = 36

Expected value and standard deviation for the sampling distribution of the sample mean can be calculated as

Expected value of sampling distribution = Population mean = 18

Standard deviation of sampling distribution of sample mean = Population standard deviation/sqrt(No. Of sample) = 5/sqrt(36) = 5/6 = 0.83

So it's answer is D. I.e. 18 and 0.83