Key Concepts

• The steps for performing a hypothesis test for two population means with unknown standard deviation are generally the same as the steps for conducting a hypothesis test for one population mean with unknown standard deviation, using a t-distribution.
• It is recommended that calculations for the test statistic and degrees of freedom be done using technology.
• Because the population standard deviations are not known, the sample standard deviations are used for calculations.
• When the sum of the sample sizes is more than 30, a normal distribution can be used to approximate the student t-distribution.
• Cohen’s d is a measure of effect size based on the differences between two means.

Glossary

Degrees of Freedom (df): the number of objects in a sample that are free to vary.

Standard Deviation: a number that is equal to the square root of the variance and measures how far data values are from their mean; notation: s for sample standard deviation and σ for population standard deviation.