Question

Obesity may be associated with lower levels of testosterone. A hypothetical study investigated this question in 60 obese males and obtained the following data.

mean testosterone (nmol/L)	0.2724
sd of testosterone	0.11153

What is the 95% confidence interval for the mean testosterone level?

Answer 1

Solution:

Given that,

n = 60

= 0.2724

s = 0.11153

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 = 60 - 1 = 59

    =    =  _0.025,59 = 2.001

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

The margin of error is given by

E =  /2,d.f. * (s / n )

= 2.001 * (0.11153 / 60)

= 0.02881132063

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

( - E ) <   <  ( + E)

(0.2724 - 0.02881132063)   <   <  (0.2724 + 0.02881132063)

0.2436 <   <  0.3012

Required 95% confidence interval is ( 0.2436 , 0.3012 )