Question

Calculate the following confidence intervals. The male confidence interval would be one calculation in the spreadsheet and the females would be a second calculation.  Mean for Females 7.666 and Standard Deviation 1.878. Mean for Males 7.764 and Standard Deviation 1.855. Total Males 17 and Total Females 18.  

1. Give and interpret the 95% confidence intervals for males and a second 95% confidence interval for females on the SLEEP variable. Which is wider and why?
2. Give and interpret the 99% confidence intervals for males and a second 99% confidence interval for females on the SLEEP variable. Which is wider and why?

Answer 1

Male :

Here n= 17, = 7.764, = 1.855

The 95% confidence interval for male is given by,

( - E, + E )

Where,

c = 0.95,

-----------( using excel formula " =norm.s.inv(0.975)" )

= 0.882

Hence the 95% confidence interval is,

( 7.764 - 0.882, 7.764 + 0.882 )

( 6.882, 8.646 )

Female:

Here n= 18, = 7.666, = 1.878

The 95% confidence interval for female is given by,

( - E, + E )

Where,

c = 0.95,

-----------( using excel formula " =norm.s.inv(0.975)" )

= 0.868

Hence the 95% confidence interval is,

( 7.666 - 0.868, 7.666 + 0.868 )

( 6.798, 8.534 )

Confidence interval for male is wider than female because margin of error of male is little larger than margin of error of female.

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Male :

Here n= 17, = 7.764, = 1.855

The 99% confidence interval for male is given by,

( - E, + E )

Where,

c = 0.99,

-----------( using excel formula " =norm.s.inv(0.995)" )

= 1.161

Hence the 99% confidence interval is,

( 7.764 - 1.161, 7.764 + 1.161 )

( 6.603, 8.925)

Female:

Here n= 18, = 7.666, = 1.878

The 99% confidence interval for female is given by,

( - E, + E )

Where,

c = 0.99,

-----------( using excel formula " =norm.s.inv(0.995)" )

= 1.142

Hence the 95% confidence interval is,

( 7.666 - 1.142, 7.666 + 1.142)

( 6.524, 8.808 )

Confidence interval for male is wider than female because margin of error of male is little larger than margin of error of female.