Question

When obtaining a confidence interval for a population mean in the case of a finite population of size N and a sample size n which is greater than 0.05N, the margin of error is multiplied by the following finite population correction factor

• Find the 95% confidence interval for the mean of 200 weights if a sample of 34 of those weights yields a mean of 155.7 lb and a standard deviation of 24.1 lb.

A.148.3 lb < p < 163.1 lb

B. 146.8 lb < p < 164.6 lb

C.147.6 lb < p < 163.8 lb

D .149.3 lb < p < 162.1 lb

Answer 1

Finite Population Correction Factor (FPC) is given by:

Given:
N = Population Size = 200

n = Sample Size = 34

Substituting, we get:

So,

=0.05

From Table, Critical Values of Z = 1.96

Margin of Error = E = 1.96 X 3.7748 = 7.3986

Confidence Interval:

155.7 7.3986

= (148.3 ,163.1)

So,

Correct option:

A.     148.3 < p < 163.1