Test for Homogeneity · Exercise 15

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.

When looking at energy consumption, we are often interested in detecting trends over time and how they correlate among different countries. The information in shows the average energy use (in units of kg of oil equivalent per capita) in the USA and the joint European Union countries (EU) for a specific six-year period. Do the energy use values in these two areas come from the same distribution? Perform the analysis at the 5% significance level.

$$\begin{array}{cccc}\text{Year}& \text{European Union}& \text{United States}& \text{Row Total}\\ \text{6}& \text{3,413}& \text{7,164}& \text{10,557}\\ \text{5}& \text{3,302}& \text{7,057}& \text{10,359}\\ \text{4}& \text{3,505}& \text{7,488}& \text{10,993}\\ \text{3}& \text{3,537}& \text{7,758}& \text{11,295}\\ \text{2}& \text{3,595}& \text{7,697}& \text{11,292}\\ \text{1}& \text{3,613}& \text{7,847}& \text{11,460}\\ \text{Column Total}& \text{20,965}& \text{45,011}& \text{65,976}\end{array}$$

This is an open-ended exercise: its source gives no single answer.

OpenStax, Introductory Statistics 2e · §11.4 Test for Homogeneity · Exercise 15