Question

A simple random sample of size n= 40 is drawn from a population. The sample mean is found to be x= 120.6 and the sample standard deviation is found to be

s 13.3 Construct a​ 99% confidence interval for the population mean.

Answer 1

solution

Given that,

= 120.6

s =13.3

n = 40

Degrees of freedom = df = n - 1 = 40- 1 = 39

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2_,df= t_0.005,39 =2.708    ( using student t table)

Margin of error = E = t_/2,df * (s /n)

=2.708 * (13.3 / 40) = 5.6947

The 99% confidence interval estimate of the population mean is,

- E < < + E

120.6 -5.6947 < < 120.6+ 5.6947

114.9053 < < 126.2947

( 114.9053 , 126.2947)