Question

Construct a 95​% confidence interval to estimate the population mean with x=118 and σ=25 for the following sample sizes.

​a) n=38

​b) n=41 ​

c) n=69

​a) With 95​% ​confidence, when n= 38​, the population mean is between the lower limit of and the upper limit of . ​(Round to two decimal places as​ needed.)

​b) With 95​% ​confidence, when n= 41​, the population mean is between the lower limit of and the upper limit of . ​(Round to two decimal places as​ needed.)

​c) With 95​% ​confidence, when n=69​, the population mean is between the lower limit of and the upper limit of . ​(Round to two decimal places as​ needed.)

Answer 1

Given that, sample mean = 118 and

population standard deviation = 25

A 95% confidence level has significance level of 0.05 and critical value is,

We want to find, the 95% confidence interval for the population mean for the following sample sizes,

a) For n = 38

Therefore, with 95​% ​confidence, when n=38, the population mean is between the lower limit of 110.05 and the upper limit of 125.95

b) For n = 41

Therefore, with 95​% ​confidence, when n=41, the population mean is between the lower limit of 110.35 and the upper limit of 125.65

c) For n = 69

Therefore, with 95​% ​confidence, when n=69​, the population mean is between the lower limit of 112.10 and the upper limit of 123.90