Sampling Distributions and t-Distribution

These flashcards cover key concepts related to sampling distributions and the t-distribution, including definitions, formulas, and important observations.

What does the central limit theorem state about sampling distributions?

As the sample size increases, the sampling distribution of the sample mean approaches a normal distribution.

When should you use the t-distribution instead of the z-distribution?

Use the t-distribution when the population variance is unknown.

What is the formula for sample variance?

Sample variance is denoted as $S^2$ and is calculated from the data.

How is the t-distribution different from the normal distribution?

The t-distribution has heavier tails than the normal distribution.

When does the t-distribution converge to the z-distribution?

The t-distribution converges to the z-distribution as the sample size $n$ approaches infinity.

What does the degrees of freedom (dof) represent in t-distribution?

Degrees of freedom is calculated as $v = n - 1$.

What is the significance of the area under the t-curve?

The area under the t-curve represents probabilities associated with t-values.

What is a critical test statistic?

A critical test statistic is a boundary value that determines the rejection region in hypothesis testing.

How can symmetry be used to find t-values?

Symmetry allows you to relate t-values for different probabilities across the horizontal axis.

In t-distribution tables, how does the area under the curve relate to t-values?

Different rows (degrees of freedom) correspond to different critical values for various areas under the curve.