Test for Homogeneity · Try It 1

(a) Do families and singles have the same distribution of cars? Use a level of significance of 0.05. Suppose that 100 randomly selected families and 200 randomly selected singles were asked what type of car they drove: sport, sedan, hatchback, truck, van/SUV. The results are shown in. Do families and singles have the same distribution of cars? Test at a level of significance of 0.05.
$$\begin{array}{cccccc}& \text{Sport}& \text{Sedan}& \text{Hatchback}& \text{Truck}& \text{Van/SUV}\\ \text{Family}& \text{5}& \text{15}& \text{35}& \text{17}& \text{28}\\ \text{Single}& \text{45}& \text{65}& \text{37}& \text{46}& \text{7}\end{array}$$
(b) Ivy League schools receive many applications, but only some can be accepted. At the schools listed in, two types of applications are accepted: regular and early decision.
$$\begin{array}{ccccccc}\text{Application type accepted}& \text{Brown}& \text{Columbia}& \text{Cornell}& \text{Dartmouth}& \text{Penn}& \text{Yale}\\ \text{Regular}& \text{2,115}& \text{1,792}& \text{5,306}& \text{1,734}& \text{2,685}& \text{1,245}\\ \text{Early decision}& \text{577}& \text{627}& \text{1,228}& \text{444}& \text{1,195}& \text{761}\end{array}$$
We want to know if the number of regular applications accepted follows the same distribution as the number of early applications accepted. State the null and alternative hypotheses, the degrees of freedom and the test statistic, sketch the graph of the χ^2 distribution and show the critical value and the calculated value of the test statistic, and draw a conclusion about the test of homogeneity.

This problem refers to a figure in its source book that isn't reproduced here.

OpenStax, Introductory Business Statistics 2e · §11.5 Test for Homogeneity · Try It 1