1 Consider a 95 confidence interval with a standard deviatio

1. Consider a 95% confidence interval with a standard deviation of 7 and a sample size of 12.

A. If the standard deviation was increased to 9 what would happen to the width of the interval?

B. If the sample size was changed to 6 what would happen to the width of the interval?

C. If the confidence decreased to 90% what would happen to the width of the interval?

D. Why is a prediction limit wider than a confidence limit given the same data and same alpha?

Solution

1) for larger std dev, width of CI will be wider

2) lower sample size will increase width

3) Decreasing level will decrease width due to lower critical values

4) prediction interval accounts for error in next observation along with past ones.