Question

Salaries of 39 college graduates who took a statistics course in college have a​ mean, x overbar​, of $ 68 comma 900. Assuming a standard​ deviation, sigma​, of ​$19 comma 972​, construct a 99​% confidence interval for estimating the population mean mu.

Answer 1

Solution:

Given,

n = 39 ....... Sample size

= 68900 ....... Sample mean

= 19972 ........population standard deviation

Note that, Population standard deviation() is known..So we use z distribution.

Our aim is to construct 99% confidence interval.

c = 0.99

= 1- c = 1- 0.99 = 0.01

  /2 = 0.01 2 = 0.005 and 1- /2 = 0.995

Search the probability 0.995 in the Z table and see corresponding z value

= 2.576   

The margin of error is given by

E =  /2 * ( / n )

= 2.576 * (19972 / 39 )

= 8238.25

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(68900 - 8238.25)   <   <  (68900 + 8238.25)

60661.75 <   <  77138.25

Required 99% Confidence interval is (60661.75 , 77138.25)