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.