## What is a T Distribution?

The T distribution and T tests are used to determine the likelihood of various conditions occurring for small sample sizes (<=30).

## How Does the T Distribution Compare with the Z Distribution?

The t distribution is flatter and wider than the z distribution.

The t distribution becomes narrower (taller) as sample sizes increase, and gradually becomes very close to the Normal Distribution. Both z and t distributions are symmetric and bell-shaped, and both have a mean of zero.

## What is the T Distribution Table?

The

http://www.sthda.com/english/wiki/t-distribution-tablet distribution tablevalues are critical values of thet distribution. The column header are thet distributionprobabilities (alpha). The row names are the degrees of freedom (df). Studentt tablegives the probability that the absolutetvalue with a given degrees of freedom lies above the tabulated value.

## When Would You Use a T Distribution or a T Distribution Table?

T-distributions are most likely used to compare two process means. It is a hypothesis test of means.

You would use these in the following specific hypothesis tests:

## Student’s T Distribution Example Questions

Student’s T distribution can used for finding confidence intervals for the population mean when the sample size is less than 30 and the population standard deviation is unknown.

### Confidence of a mean 1

At a soda bottling factory, the normal filling specification (goal) is 16 fluid ounces. A sample of 20 bottles is tested with the following results: x = 16.13 fl oz and s = 0.24 fl oz. What interval would allow you to say, with 95% confidence, that the interval contains the actual mean of the filling process?

### Confidence of a mean 2

An automated computer attendant is supposed to respond to all inquiries within 15 seconds. The company claims with 99 percent confidence that the average response time is less than 17 seconds. A random sample of 25 calls reveals that X = 13.5 seconds and s = 0.95 seconds. Based on this data is the company correct?

### Confidence of a mean 3

A photography developing machine uses ink to produce photographs. A sample of 15 pictures showed an average of 1.5 mL of ink used per picture, with a standard deviation o 0.075 mL. Develop a 99% confidence band for the actual average amount of ink used by the machine to produce each photograph.