Question

Construct the confidence interval for the population mean μ.

c = 0.90​, x = 15.5​, s = 2.0, and n = 65

A 90​% confidence interval for μ is ( ____ , ____ ).

Answer 1

Solution :

Given that,

= 15.5

s = 2.0

n = 65

c = 0.90

Degrees of freedom = df = n - 1 = 65 - 1 = 64

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

t _/2,df = t_0.05,64=1.669

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

= 1.669 * (2.0/ 65) = 0.5151

The 90% confidence interval estimate of the population mean is,

- E < < + E

15.5 - 0.5151 < <15.5 + 0.5151

14.9849 < < 16.0151

(14.9849 , 46.0151)