The chi-square discussion in Chapter 8 provides a means of assessing whether two or more categorical variables are statistically independent of one another. This chapter takes up the t test. The t test is a means of assessing whether a numerical variable—either continuous or discrete—is independent of a categorical variable that takes on only two values. The t test provides another capability. It provides the ability to assess whether a value found from a sample could have come from a population in which a hypothesized value is true. This chapter addresses both of these issues, beginning with the latter.

9.1 What Is a t Test?

To begin with a discussion of the t test, recall the question addressed by the hospital financial officer in Chapter 7. The CFO wished to know the true average cost of a hospital discharge. He decided to take a sample of 100 discharge records. He then calculated the true cost of each hospital stay. In turn, he used the mean cost of this sample of discharges as the mean cost for all 12,000 hospital stays. Suppose that ...

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