Test for Homogeneity · Exercise 13

In a recent year, the United States had 1.5 million homeschooled students, according to the U.S. National Center for Education Statistics. In you can see that parents decide to homeschool their children for different reasons, and some reasons are ranked by parents as more important than others. According to the survey results shown in the table, is the distribution of applicable reasons the same as the distribution of the most important reason? Provide your assessment at the 5% significance level. Did you expect the result you obtained?

$$\begin{array}{cccc}\text{Reasons for Homeschooling}& \text{Applicable reason (in thousands of respondents)}& \text{Most important reason (in thousands of respondents)}& \text{Row total}\\ \text{Concern about the environment of other schools}& \text{1,321}& \text{309}& \text{1,630}\\ \text{Dissatisfaction with academic instruction at other schools}& \text{1,096}& \text{258}& \text{1,354}\\ \text{To provide religious or moral instruction}& \text{1,257}& \text{540}& \text{1,797}\\ \text{Child has special needs, other than physical or mental}& \text{315}& \text{55}& \text{370}\\ \text{Nontraditional approach to child’s education}& \text{984}& \text{99}& \text{1,083}\\ \text{Other reasons (e.g., finances, travel, family time, etc.)}& \text{485}& \text{216}& \text{701}\\ \text{Column total}& \text{5,458}& \text{1,477}& \text{6,935}\end{array}$$

Its source prints no answer for this problem, so there's nothing to check against.

OpenStax, Introductory Business Statistics 2e · §11.5 Test for Homogeneity · Exercise 13