Lesson 9: Inference for Two Samples
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
We will be using a five step hypothesis testing procedure again in this lesson:
- 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., \(=\)).
- 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.
- Determine the \(p\) value
This can be found using Minitab Express.
- Make a decision
If \(p \leq \alpha\) reject the null hypothesis. If \(p>\alpha\) fail to reject the null hypothesis.
- State a "real world" conclusion
Based on your decision in step 4, write a conclusion in terms of the original research question.