Question

20 principals are selected and the sample mean is 58 years old. The standard deviation 8 years. Construct the 95 confidence interval.

Answer 1

Solution :

Given that,

= 58

s = 8

n = 20

Degrees of freedom = df = n - 1 = 20 - 1 = 19

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,19 = 2.093

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

= 2.093 * (8 / 20)

= 3.744

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

- E < < + E

58 - 3.744 < < 58 + 3.744

54.256 < < 61.744

(54.256, 61.744)