Key Concepts

• When doing any hypothesis test, the data should come from a random sample.
• When doing a hypothesis test for a mean, a t-distribution is used when the sample size is small or you are using the sample standard deviation. This is called a t-test for a mean.
• When doing a hypothesis test for a mean, a normal distribution is used when the sample size is large and the population standard deviation is known. This is called a z-test for a mean.
• When doing a hypothesis test for a proportion, a normal distribution is used. However, [latex]np[/latex] and [latex]nq[/latex] must be both greater than 5. This is called a z-test for a proportion.

Glossary

Student’s t-Distribution: Investigated and reported by William S. Gossett in 1908 and published under the pseudonym Student. The major characteristics of the random variable (RV) are:

• It is continuous and assumes any real values.
• The pdf is symmetrical about its mean of zero. However, it is more spread out and flatter at the apex than the normal distribution.
• It approaches the standard normal distribution as n gets larger.
• There is a “family” of t distributions. Every representative of the family is completely defined by the number of degrees of freedom, which is one less than the number of data items.