Question

One can calculate the 95% confidence interval for the mean with the population standard deviation known. This will give us an upper and a lower confidence limit. What happens if we decide to calculate the 99% confidence interval? Describe how the increase in the confidence level has changed the width of the confidence interval. Do the same for the confidence interval set at 80%. Include an example with actual numerical values for the intervals in your post to help with your explanations.

Answer 1

Sol:

let us say sample mean=xbar=25

sample size=n=100

popualtion standard deviation=sigma=10

z crit for 99%=2.576

99% confidene interval for mean

xbar-z*sigma/sqrt(n),xbar+z*sigma/sqrt(n)

25-2.576*10/sqrt(100),25+2.576*10/sqrt(100)

22.424,27.576

similary

z crit for 95%=1.96

95% confidene interval for mean

xbar-z*sigma/sqrt(n),xbar+z*sigma/sqrt(n)

25-1.96*10/sqrt(100),25+1.96*10/sqrt(100)

23.04, 26.9

z crit for 80%=1.28

80% confidene interval for mean

xbar-z*sigma/sqrt(n),xbar+z*sigma/sqrt(n)

25-1.28*10/sqrt(100),25+1.28*10/sqrt(100)

23.72,26.28

width of the onterval increases when we change from 80 t to 99% as z critical increases