Chapter 11, Problem 1SE

In Exercises 11.1 and 11.2, for each situation, choose the appropriate test: one-sample $t$ -test, two-sample $t$ -test, ANOVA, or chi-square test.

a. You want to test whether there is an association between a categorical variable and a

numerical variable. For example, you want to test whether there is an association between type

of apartment (studio, one-bedroom, or two-bedroom) and monthly rent.

b. You want to test whether the means of a numerical variable are different for two possible

values of a categorical variable. For example, you want to test whether the mean income of

paramedics is the same for male and female paramedics.

To determine

Determine the appropriate test for the following situations:

a. To test whether there is an association between type of apartment and monthly rent.

b. To test whether the mean income of paramedics is same for male and female paramedics.

Answer to Problem 1SE

a. ANOVA test is used to test the association between type of apartment (categorical variable) and monthly rent (numerical variable).

b. Two sample t-test is used to test whether the mean income of paramedics is same for male and female paramedics.

Explanation of Solution

a.

ANOVA is a parametric statistical test which is used to test the differences among the group means in sample or population. In ANOVA test we assumed that the sample is drawn from normally distributed population and the population variance is equal.

In the provided case one variable is numeric (monthly rent) and other variable is categorical (studio, one-bedroom, two-bedroom). So, there are 3 groups and ANOVA is the only parametric test which is used to compare the means of more than two populations.

b.

Two-sample $t\text{-}$ test is used to test whether the population means of two independent groups are equal or not. So, two-sample $t\text{-}$ test is a suitable test to test whether the mean income of paramedics of male and female categories is equal or not.