Question

Construct the confidence interval for the population mean μ.

c=0.95, x= 9.5,σ=0.8​,and n=44

A 95​% confidence interval form μ is(_,_) ​(Round to two decimal places as​ needed.)

Answer 1

c = 0.95

α = 1 - c = 1 - 0.95 = 0.05

α/2 = 0.05/2 = 0.025

1 - α/2 = 0.975

Therefore z score corresponding to 0.975 on z score table is 1.96

z = 1.96

Given : = 9.5 , σ = 0.8​,and n = 44

Confidence interval is given by,

Lower bound =   - E  

Upper bound =   + E  

E is margin of error =   = = 0.2364

Lower bound = 9.5 - 0.2364 = 9.26

Upper bound = 9.5 + 0.2364 = 9.74

A 95​% confidence interval form μ is (9.26 , 9.74)