Question

A simple random sample of 25 items from a normally distributed population resulted in a sample mean of 80 and a sample standard deviation of s=7.5. Construct a 95% confidence interval for the population mean.

Answer 1

Solution:

Given that,

n = 25

= 80

s = 7.5

Note that, Population standard deviation() is unknown. So we use t distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, d.f = n - 1 = 25 - 1 = 24

    =    =  _0.025,24 = 2.064

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n )

= 2.064 * (7.5 / 25)

= 3.096

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

( - E ) <   <  ( + E)

(80 - 3.096)   <   <  (80 + 3.096)

76.904 <   <  83.096

i.e.

(76.904 , 83.096)