Question

Given a sample size 18 with a 99% confidence interval for the mean μ, and a known standard deviation (26.64, 33.25), calculate the 95% confidence interval for μ.

Answer 1

Solution :

Given that,

μ = = 26.64

s =33.25

n = Degrees of freedom = df = n - 1 = 18- 1 = 17

At 95% confidence level the t is ,

= 1 - 95% = 1 - 0.95 = 0.05

  / 2= 0.05 / 2 = 0.025

t /2,df = t0.025,17 =1.812 ( using student t table)

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

= 1.812 * (33.25/ 18)

= 14.20

The 95% confidence interval mean is,

- E < < + E

26.64 - 14.20 < < 26.64+ 14.20

12.44 < < 40.84

95% confidence interval for μ is (12.44, 40.84)