Question

A random sample of 150 students is chosen from a population of 5,000 students. If the mean IQ in the sample is 110 with a standard deviation of 10, what is the 95% confidence interval for the students' mean IQ score?

Answer 1

(106.805, 113.195)

Explanation:

Given that A random sample of 150 students is chosen from a population of 5,000 students.

Mean of sample is 110 and std dev =10

s=10

Std error of sample = 20/sqrt 150

=20/12.25

=1.63

Mean = 110

Since confidence level is 95% z = 1.96

Margin of error = 1.96 (std error) =3.195

Confidence interval lower bound = mean-3.195 = 106.805

Upper bound = mean+3.195 = 113.195

Answer 2

The critical value for a 95% C.I. is about
`z_(0.95)=1.96`, so the 95% C.I. for this sample is


`110\pm1.96(10)/(√(150))=(108.4,111.6)`