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)

When population standard deviation known Z distribution is used

Z value for 95% CI =1.96

Let us take mean =30 standard deviation =4 and sample size =64

Confidence interval = mean z*sd/sqrt(n)

Sd/sqrt(n) =4/sqrt(64) =0.5

95% CI =(30-1.96*0.5, 30+1.96*0.5) =(29.02, 30.98)

Z value for 99% CI =2.576

99% CI =(30-2.576*0.5, 30+2.576*0.5) =(28.712, 31.288)

When the confidence level increases, the width of the confidence interval increases.

Z value for 80% CI =1.282

80% CI =(30-1.282*0.5, 30+1.282*0.5) =(29.359, 30.641)

When the confidence level decreases, the width of the confidence interval decreases.