Question

A simple random sample of size n is drawn from a population that is normally distributed. The sample​ mean, x overbar​, is found to be 111​, and the sample standard​ deviation, s, is found to be 10. ​(a) Construct a 95​% confidence interval about mu if the sample​ size, n, is 26.

Answer 1

Solution :

Given that,

= 111

s =10

n =26

Degrees of freedom = df = n - 1 = 26- 1 = 25

a ) At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,25 = 2.060 ( using student t table)

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

=2.060 * (10 / 26)

= 4.0400

The 95% confidence interval estimate of the population mean is,

- E < < + E

111 -4.0400 < <111 + 4.0400

106.9600 < < 115.0400

(106.9600 ,115.0400 )