Chapter 9: Statistical Inference Based on Two Samples

Hypothesis Testing for Means

In this chapter we will again make use of the Excel file of weight reductions using the Atkins diet vs. the conventional diet over a six month period.

[9.1 & 9.2] Assumption : Variances are known.

When the variances are known, we use HT results that are similar to those in Chapter 8. [We will not cover Section 9.2 in 2013.]

We will not cover these sections in 2013. [9.3 & 9.4] Assumption : Variances are not known, but equal.

Once again, this requires the t-test, and that later, we will test the hypothesis that the variances are in fact equal (or not).

We will not cover this section in 2013. [9.5] z-Tests about a Difference in Populations Proportions <This section [9.5] is not included in the exam, but we will nevertheless do an experiment in class (not in 2013) and use MegaStat to illustrate the material here. (Otherwise, this chapter will turn into a very dry one.) >

[9.6] F-test for equality of variances

This test (due to Ronald Fisher, of the ``Lady Tasting Tea'' fame) should be used when the assumption of equality of variances is made. If the null hypothesis is true, then the ratio of the two sample variances has F-distribution. F-table needed to do the test is here.

In the example, we again use the Excel file of weight reductions using the Atkins diet vs. the conventional diet over a six month period. Here, we have n₁ = 33 and n₂ = 30 samples which had sample standard deviations of 14.37 and 12.36, resp. We will show that we cannot reject the null hypothesis of equality of variances. So, the assumption we made above seems valid.