Question

1. Calculate the 99%, 95%, and 90% confidence intervals for the following information. Identify how these confidence intervals are similar and how they are different. Explain why. (70 points)

µ = 89 σ = 9 n = 121

1. The 99% Confidence Interval:

2. The 95% Confidence Interval:

3. The 90% Confidence Interval:

4. Similarities:

5. Differences:

6. Why?

Answer 1

1) The 90% confidence  interval is ,

Margin of error=E=1.3418

Width of the confidence interval=90.3418-87.6582=2.6836

2) The 95% confidence interval is ,

Margin of error=E=1.6037

Width of the confidence interval=90.6037-87.3963=3.2074

3) The 99% confidence interval is ,

Margin of error=E=2.1110

Width of the confidence interval=91.1110-86.8890=4.2220

4) The standard error is similar. S.E.=

5) Now , the confidence intervals are different because as the confidence level increases , then the margin of error increases.

Also , as the confidence level increases , then the width of the confidence interval increased.