Inference for the Difference Between Two Population Means for AP Statistics

Practice problems for these concepts can be found at:

• Inference for Means and Proportions Multiple Choice Practice Problems for AP Statistics
• Inference for Means and Proportions Free Response Practice Problems for AP Statistics
• Inference for Means and Proportions Review Problems for AP Statistics
• Inference for Means and Proportions Rapid Review for AP Statistics

The two-sample case for the difference in the means of two independent samples is more complicated than the one-sample case. The hypothesis testing logic is identical, however, so the differences are in the mechanics needed to do the problems, not in the process. For hypotheses about the differences between two means, the procedures are summarized in the following table.

Notes on the above table:

• Generally speaking, you should not assume the population variances are equal. The bottom line in the table gives the conditions and test statistic if you can make the necessary assumption. The problem is that it is very difficult to justify the assumption.
• The middle rows for conditions and test statistic give the typical t-procedure approach. The first way of computing degrees of freedom is the "conservative" method introduced in Chapter 11. The "software" method is based on the formula given in Chapter 11.

example: A statistics teacher, Mr. Srednih, gave a quiz to his 8:00 AM class and to his 9:00 AM class. There were 50 points possible on the quiz. The data for the two classes were as follows.

Before the quiz, some members of the 9:00 AM class had been bragging that later classes do better in statistics. Considering these two classes as random samples from the populations of 8:00 AM and 9:00 AM classes, do these data provide evidence at the .01 level of significance that 9:00 AM classes are better than 8:00 AM classes?

solution:

Practice problems for these concepts can be found at:

• Inference for Means and Proportions Multiple Choice Practice Problems for AP Statistics
• Inference for Means and Proportions Free Response Practice Problems for AP Statistics
• Inference for Means and Proportions Review Problems for AP Statistics
• Inference for Means and Proportions Rapid Review for AP Statistics