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.**

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