Question

A random sample of size n = 472 is taken from a population of size N = 9,700 with mean μ = −63 and variance σ2 = 176. [You may find it useful to reference the z table.]

A-1

Is it necessary to apply the finite population correction factor?

• Yes

• No

a-2. Calculate the expected value and the standard error of the sample mean. (Negative values should be indicated by a minus sign. Round "standard error" to 2 decimal places.)

Expected Value-

Standard Error-

Answer 1

a -1) Given N = 9700 , n = 472

n/N = 472/9700 < 0.05

So finite population correction factor can not be applied.

a - 2) expected value and standard error of sample mean is

Expected value = $\large \mu$ = -63

Standard Error = $\large \sigma$ /√n = 13.27/√472 = 0.61