Question

IQ tests are designed to yield results that are approximately Normally distributed. Researchers think believe that the standard deviation, σ, is 15. A reporter is interested in estimating the average IQ of employees in a large high-tech firm in California. She gathers the IQ information on 22 employees of this firm and recoreds the sample mean IQ as 106. Let X represent a random variable describing a person's IQ: X~N(µ, 15).

a. Find the standard error of the sample mean.

b. Calculate a 90% confidence interval.

c. Interpret the confidence interval in the context of the problem.

( Need excel form )

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 106

Population standard deviation =    = 15

Sample size = n = 22

a) = / n = 15 / 22 = 3.20

At 90% confidence level

= 1 - 90%  

= 1 - 0.90 =0.10

/2 = 0.05

Z/2 = Z0.05 = 1.645

Margin of error = E = Z/2 *

= 1.645 * 3.20

= 5.26

b) At 90% confidence interval estimate of the population mean is,

  ± E

106 ± 5.26

( 100.74, 111.26 )  

c) We are 90% confident that the true mean of  employees in a large high-tech firm in California between 100.74 and 111.26