## 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.

### Difference between Means

#### Questions

**Question 1 out of 4.**

Select all of the assumptions that you need to make when creating a confidence interval on the difference between means.

At least 2% of the population sampled

Independently sampled values

Homogeneity of variance

Normally distributed populations

**Question 2 out of 4.**

You are comparing men and women on hours spent watching TV. You pick a sample of 12 men and 14 women and calculate a confidence interval on the difference between means. How many degrees of freedom does your t value have?

**Question 3 out of 4.**

**Question 4 out of 4.**

Scores on a test taken by 1st graders and 2nd graders were compared to look at development. The five 1st graders sampled got the following scores: 4, 3, 5, 7, 4. The five 2nd graders sampled got the following scores: 7, 9, 8, 6, 9. Compute the 95% confidence interval for the difference between means (2nd graders - 1st graders). You may use the Analysis Lab. What is the upper limit?

Grade Score 1 4 1 3 1 5 1 7 1 4 2 7 2 9 2 8 2 6 2 9