Let’s Summarize

• The steps for performing a hypothesis test for two population means with unknown standard deviation is generally the same as the steps for conducting a hypothesis test for one population mean with unknown standard deviation, using a t-distribution.
• 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’s t-distribution.
• The difference of two proportions is approximately normal if there are at least five successes and five failures in each sample.
• When conducting a hypothesis test for a difference of two proportions, the random samples must be independent and the population must be at least ten times the sample size.
• When calculating the standard error for the difference in sample proportions, the pooled proportion must be used.
• When two measurements (samples) are drawn from the same pair of individuals or objects, the differences from the sample are used to conduct the hypothesis test.
• The distribution that is used to conduct the hypothesis test on the differences is a t-distribution.