Test for Homogeneity · Exercise 16

For each word problem, use a solution sheet to solve the hypothesis test problem. Go to for the chi-square solution sheet. Round expected frequency to two decimal places.

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 the two years 2009 and 2013. Analyze the table data to conclude whether the distribution of cars that earned the top safety picks safety award has remained the same between 2009 and 2013. Derive your results at the 5 percent significance level.

$$\begin{array}{cccccccc}\text{Year/Car Type}& \text{Small}& \text{Mid-Size}& \text{Large}& \text{Small SUV}& \text{Mid-Size SUV}& \text{Large SUV}& \text{Row Total}\\ \text{2009}& \text{12}& \text{22}& \text{10}& \text{10}& \text{27}& \text{6}& \text{87}\\ \text{2013}& \text{31}& \text{30}& \text{19}& \text{11}& \text{29}& \text{4}& \text{124}\\ \text{Column Total}& \text{43}& \text{52}& \text{29}& \text{21}& \text{56}& \text{10}& \text{211}\end{array}$$

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

OpenStax, Statistics · §11.4 Test for Homogeneity · Exercise 16