T Distribution
Photo by: JD Hancock

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 t distribution table values are critical values of the t distribution. The column header are the t distribution probabilities (alpha). The row names are the degrees of freedom (df). Student t table gives the probability that the absolute t value with a given degrees of freedom lies above the tabulated value.

http://www.sthda.com/english/wiki/t-distribution-table

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?

Student 1
Student 1 chart

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?

Student 2 chart
Student 2

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.

Student 3 chart
Student 3

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