Lesson 8: Inference for One Sample

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This lesson corresponds to Chapter 6 in the Lock^5 textbook.

Lesson 8 Learning Objectives

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

  • identify situations in which the normal (z) distribution, binomial distribution, and t distribution should be applied to construct a confidence interval or conduct a hypothesis test.
  • determine the necessary minimum sample size to construct a confidence interval with a given level of confidence and given margin of error. 
  • construct confidence intervals to estimate a population proportion or population mean using Minitab Express.
  • conduct a hypothesis test 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:

  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.

Some steps may vary depending on the test.

We will be relying heavily on Minitab Express in this lesson and all of the following lessons. Note that help is avaliable in Minitab Express. In any of the dialog boxes there is a button to click that will take you to a relevant page on the Minitab Express help website:

Minitab Express Help Button