# Lesson 9: Inference for Two Samples

## Objectives

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

• Identify situations in which the z or t distribution may be used to approximate a sampling distribution
• Construct a confidence interval to estimate the difference in two population proportions and two population means using Minitab Express given summary or raw data
• Conduct a hypothesis test for two proportions and two means using Minitab Express given summary or raw data

Note: This lesson corresponds to Chapter 6: Sections 3 and 4 in the Lock5 textbook.

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.