Test for Homogeneity · Exercise 15

The Insurance Institute for Highway Safety collects safety information about all types of cars every year, and publishes a report of Top Safety Picks among all cars, makes, and models. presents the number of Top Safety Picks in six car categories for specific two years. Analyze the table data to conclude whether the distribution of cars that earned the Top Safety Picks safety award has remained the same between Year 1 and Year 2. Derive your results at the 5% significance level.

$$\begin{array}{cccccccc}\text{Year Car type}& \text{Small}& \text{Mid-size}& \text{Large}& \text{Small SUV}& \text{Mid-size SUV}& \text{Large SUV}& \text{Row total}\\ \text{Year 1}& \text{12}& \text{22}& \text{10}& \text{10}& \text{27}& \text{6}& \text{87}\\ \text{Year 2}& \text{31}& \text{30}& \text{19}& \text{11}& \text{29}& \text{4}& \text{124}\\ \text{Column total}& \text{43}& \text{52}& \text{29}& \text{21}& \text{56}& \text{10}& \text{211}\end{array}$$

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 15