Statistical Applets Distribution of the one-sample t statistic

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.	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.

Statistical Applets

Distribution of the one-sample t statistic

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.

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.