## Confidence Intervals for the Mean

This section explains the need for confidence intervals and why a confidence interval is not the probability the interval contains the parameter. Then, it discusses how to compute a confidence interval on the mean when sigma is unknown and needs to be estimated. It also explains when to use t-distribution or a normal distribution. Next, it covers the difference between the shape of the t distribution and the normal distribution and how this difference is affected by degrees of freedom. Finally, it explains the procedure to compute a confidence interval on the difference between means.

### Confidence Interval on the Mean

#### Questions

**Question 1 out of 5.**

**Question 2 out of 5.**

**Question 3 out of 5.**

(37.49, 38.51)

(36.49, 39.51)

(35.45, 40.55)

**Question 4 out of 5.**

(39.76, 58.24)

(44.53, 53.47)

(45.93, 52.07)

**Question 5 out of 5.**

Based on the data below, what is the upper limit of
the 95% confidence interval for the mean of A1? You may want to use the
Analysis Lab or another statistical program to answer this.

________

A1 1 4 5 5 7 9 10 11 12 13 14 14 17 19 20 23 24 24 24

29