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.

A t distribution with which of the following degrees of freedom is the closest to a normal distribution?

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.

There is a population of test scores with an unknown standard deviation. You sample 21 scores from this population, and you calculate the mean and standard deviation. You get a value for the mean that is 1.5 standard errors greater than what you think is the population mean. What is the probability that you would get a value 1.5 standard deviations or more from the mean in this t distribution?