Chapter 1. Distribution of the one-sample t statistic

Statistical Applets

Choose a population distribution (Exponential, Uniform, or Normal) and a sample size, then click the button to generate 10,000 samples and a histogram of the resulting t statistics. Click "Show t curve" to compare this histogram with the t distribution with n-1 degrees of freedom.

When a simple random sample (SRS) of size n is drawn from a N(μ, σ) population, the one-sample t statistic has the t distribution with n-1 degrees of freedom. How close is the distribution of the t statistic to the t distribution when the population is not Normal?

This applet allows you to generate thousands of samples with various sizes n from an exponential, uniform, or Normal population distribution. You can then compare the distribution of t statistics against the t distribution used in the one-sample t test.

1.

When n = 2, the sampling distribution for the population with the exponential distribution is , whereas when n = 50, the sampling distribution for the exponential population is .

2
Try again.
Incorrect. See above for the correct answers.
Great job.

2.

When n = 3, which of the following statements best describes how the distribution of sample means from the Uniform distribution varies compared to the Normal curve predicted by the Central Limit Theorem?

A.
B.
C.
2
Correct.
Try again.
Incorrect.

3.

Describe in your own words how the shapes of the sampling distributions compare for the three population distributions when n = 100:
The sampling distribution for the exponential population distribution might still be very slightly skewed to the left, but other than this the shapes of the three distributions are virtually identical Normal-shaped curves.