Question

If Upper X overbar = 90​, σ = 9​, and n = 68​, construct a 95​% confidence interval estimate of the population​ mean, μ.

______ ≤ μ ≤ _____

​(Round to two decimal places as​ needed.)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 90

Population standard deviation =    = 9

Sample size = n =68

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.96

Margin of error = E = Z/2 * ( /n)

= 1.96 * (9 /  68 )

= 2.1392
At 95% confidence interval estimate of the population mean
is,

- E < < + E

90 - 2.1392 <   < 90 + 2.1392

87.86 <   < 92.14