Question

The random sample shown below was selected from a normal distribution. 5 ​, 3 ​, 7 ​, 6 ​, 6 ​, 9 Complete parts a and b.
a. Construct a 99 ​% confidence interval for the population mean mu . left parenthesis nothing comma nothing right parenthesis ​(Round to two decimal places as​ needed.)
b. Assume that sample mean x overbar and sample standard deviation s remain exactly the same as those you just calculated but that are based on a sample of n=25 observations.
Repeat part a. What is the effect of increasing the sample size on the width of the confidence​ intervals? The confidence interval is left parenthesis nothing comma nothing right parenthesis . ​(Round to two decimal places as​ needed.)
What is the effect of the sample size on the width of the confidence​ interval?

Answer 1

a)

99 ​% confidence interval for the population mean =(2.71 ; 9.29)

b)

99 ​% confidence interval for the population mean =(4.39 ; 7.61)

as we increase the sample size ; confidence interval width reduces due to reduction in std error of mean