Question

Construct the indicated confidence interval for the population mean mu? using a? t-distribution.

c=0.95, x =110,s= 10, n=27

The confidence interval is

?(Round to the nearest tenth as? needed.)

Answer 1

Solution :

Given that,

= 110

s = 10

n = 27

c = 0.95

Degrees of freedom = df = n - 1 = 27 - 1 = 26

= 1 - 0.95 = 0.05

  / 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,26 = 2.056

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

= 2.056 * (10 / 27) = 3.96

The confidence interval estimate of the population mean is,

- E < < + E

110 - 3.96 < < 110 + 3.96

106.04 < < 113.96

(106, 114 )