# Levels of Confidence and Intervals

1. Find the level of confidence assigned to an interval estimate of the mean formed using the interval: x − 1.96⋅σx to x + 1.96⋅σ x .

2. The lengths of 225 fish caught in Lake Michigan had a mean of 15.0 inches. Assume that the population standard deviation is 2.5 inches.

- Give a point estimate for μ .

- Find the 90% confidence interval for the population mean length.

3. In an effort to compare college costs in State of Michigan, a sample of 36 junior students is randomly selected statewide from the private colleges and 36 more from the public colleges. The private college sample resulted in a mean of $27,650 and the public college sample mean was $11,360. Assume the annual college fees for private colleges have a mounded distribution and the standard deviation is $1725. Find the 95% confidence interval for the mean costs for private colleges.

4. What effect does an increase in the level of confidence have on the width of the confidence interval?

5. You are constructing a 95% confidence interval using the following information: n = 60, = 65.5, s = 2.5, and E = 0.7. What is the value of the middle of the interval?

A) 0.7

B) 2.5

C) 0.95

D) 65.5

#### Solution Preview

1. Find the level of confidence assigned to an interval estimate of the mean formed using the interval: x − 1.96⋅σx to x + 1.96⋅σ x .

Solution. We know that the z-score is z=1.96. So, the confidence level is 1-alpha=95%.

2. The lengths of 225 fish caught in Lake Michigan had a mean of 15.0 inches. Assume that the population standard deviation is 2.5 inches.

• Give a point estimate for μ .

We can use the sample mean as a point estimate for μ.

• Find the 90% confidence interval ...

#### Solution Summary

The solution examines levels of confidence and intervals for college costs in the State of Michigan.