# Lesson 9: Inference for Two Samples

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This lesson corresponds to Chapter 6 sections 3 and 4 in the Lock^5 textbook.

### Lesson 9 Learning Objectives

Upon completion of this lesson, you should be able to:

• identify situations in which the normal, binomial, and t distributions should be applied to construct a confidence interval and conduct a hypothesis test for the difference between two proportions and difference in two means.
• construct a confidence interval to estimate the difference in two population proportions and two population means using Minitab Express.
• conduct a hypothesis test for two proportions and two means using the appropriate common distribution in Minitab Express

The general form of confidence intervals and test statistics will be the same for all of the procedures covered in this lesson:

General Form of a Confidence Interval

sample statistic $$\pm$$ (multiplier) (standard error)

General Form of a Test Statistic

$test\;statistic=\frac{sample\;statistic-null\;parameter}{standard\;error}$

We will be using a five step hypothesis testing procedure again in this lesson:

1. Check assumptions and write hypotheses. The assumptions will vary depending on the test. The null and alternative hypotheses will also be written in terms of population parameters; the null hypothesis will always contain the equality (i.e., $$=$$).
2. Calculate the test statistic. This will vary depending on the test, but it will typically be the difference observed between the sample and population divided by a standard error. In this lesson we will see z and t test statistics. Minitab Express will compute the test statistic.
3. Determine the p value. This can be found using Minitab Express.
4. Make a decision. If $$p \leq \alpha$$ reject the null hypothesis. If $$p>\alpha$$ fail to reject the null hypothesis.
5. State a "real world" conclusion. Based on your decision in step 4, write a conclusion in terms of the original research question.