a A statistics practitioner took a random sample of 50 obser

a. A statistics practitioner took a random sample of 50 observations from a population                whose standard deviation is 25 and computed the sample mean to be 100. Estimate the population mean with 90% confidence.

b. Repeat Part a using a 95% confidence level.

c. Repeat Part a using a 99% confidence level.

d. Describe the effect on the confidence interval estimate of increasing the confidence level.

Solution

Since the \"population\" standard deviation is provided, you can use a z-Interval ...

CI = mean +/- (z*) (standard deviation) / sqrt n

where z* = 1.645, 1.96 and 2.576 for 90%, 95% and 99%, respectively from the Standard Normal table.

Now use the formula above ...

1.) Use an interval estimate to estimate the population mean with 90% confidence

[94.18, 105.82]

2.) Repeat part a. using a 95% confidence level.

[93.07, 106.93]

3.) Repeat part a. using a 99% confidence level.

[90.89, 109.11]

4) AS WE INCREASE THE CONFIDENCE LEVEL THE INTERVAL SETS TO BE INCREASED
hope that helped