Question

A psychologist is interested in the mean IQ score of a given group of children. It is known that the IQ scores of the group have a standard deviation of 11

. The psychologist randomly selects 150 children from this group and finds that their mean IQ score is 99 . Based on this sample, find a 95% confidence interval for the true mean IQ score for all children of this group. Then complete the table below.

What is the lower limit of the 95% confidence interval?
What is the upper limit of the 95% confidence interval?

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 99

Population standard deviation =    = 11

Sample size = n = 150

At 95% confidence level

= 1 - 95%  

= 1 - 0.95 =0.05

/2 = 0.025

Z/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * ( 11 /  150 )

= 1.76

At 95% confidence interval estimate of the population mean is,

  ± E

= 99 ± 1.76   

( 97.24 , 100.76)  

lower limit = 97.24

upper limit = 100.76