Lesson 5: Hypothesis Testing, Part 1

Objectives

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

• Identify and write null and alternative hypotheses
• Describe randomization procedures
• Determine p-values using randomization methods in StatKey and Minitab Express
• Interpret p-values
• Make conclusions on the basis of a p-value

In Lesson 4 we used data from samples to construct confidence intervals for population parameters. When constructing confidence intervals the population parameters were unknown and we were estimating them. In this lesson we will continue to study statistical inference, but here we will be focusing on testing specific hypotheses. Now, we have a hypothesized population parameter to test. This changes how we construct our sampling distribution. Instead of having a distribution centered on the observed sample statistic, we will construct a distribution centered on the hypothesized population parameter.

This lesson corresponds to Sections 4.1, 4.2, and 4.3 in the Lock5 textbook.

Hypothesis tests use data from a sample to make an inference about the value of a population parameter. In this lesson we will be conducting hypothesis tests with the following parameters:

Population Parameter Sample Statistic
Mean $$\mu$$ $$\overline x$$
Difference in two means $$\mu_1 - \mu_2$$ $$\overline x_1 - \overline x_2$$
Proportion $$p$$ $$\widehat p$$
Difference in two proportions $$p_1 - p_2$$ $$\widehat p_1 - \widehat p_2$$
Correlation $$\rho$$ $$r$$
Slope (simple linear regression) $$\beta$$ $$b$$

We can also conduct hypothesis tests with paired means. If data are paired, and the response variable is quantitative, then the outcome of interest is the mean difference. In a population this is $$\mu_d$$ and in a sample $$\overline x_d$$. We would first compute the differences for each case, then treat those differences as if they are the variable of interest and conduct a single sample mean test.