# Lesson 8: Inference for One Sample

## Objectives

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

• Identify situations in which the z or t distributions may be used to approximate a sampling distribution
• Construct a confidence interval to estimate a population proportion, mean, or difference in paired means by hand given summary data
• Construct a confidence interval to estimate a population proportion, mean, or difference in paired means using Minitab Express given summary or raw data
• Determine the necessary minimum sample size to construct a confidence interval for a single proportion or single mean with a given level of confidence and margin of error
• Conduct a hypothesis test using the appropriate common distribution for a single proportion, single mean, and paired means by hand given summary data
• Conduct a hypothesis test using the appropriate common distribution for a single proportion, single mean, and paired means using Minitab Express given summary or raw data

This lesson corresponds to Chapter 6 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
$$test\;statistic=\dfrac{sample\;statistic-null\;parameter}{standard\;error}$$

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: