## 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.

### t Distribution

#### Questions

**Question 1 out of 5.**

Select all of the following that are correct descriptions of the t distribution.

There are more scores in the tails than in a normal distribution. There are more scores in the center than in a normal distribution.

It is leptokurtic.

You use it when you do not know the population standard deviation.

A t distribution with 20 degrees of freedom has 95% of its distribution within 1.96 standard deviations of its mean.

**Question 2 out of 5.**

0

2

12

50

**Question 3 out of 5.**

For a t distribution with 15 degrees of freedom, 90% of the distribution is within how many standard deviations of the mean?

**Question**

**4 out of 5.**

In a t distribution with 10 degrees of freedom, what is the probability
of getting a value within two standard deviations of the mean?

**Question 5 out of 5.**