Test of Independence · Exercise 7

Transit Railroads is interested in the relationship between travel distance and the ticket class purchased. A random sample of 200 passengers is taken. shows the results. The railroad wants to know if a passenger’s choice in ticket class is independent of the distance the passenger must travel.
$$\begin{array}{ccccc}\text{Traveling Distance}& \text{Third Class}& \text{Second Class}& \text{First Class}& \text{Total}\\ \text{1–100 miles}& \text{21}& \text{14}& \text{6}& \text{41}\\ \text{101–200 miles}& \text{18}& \text{16}& \text{8}& \text{42}\\ \text{201–300 miles}& \text{16}& \text{17}& \text{15}& \text{48}\\ \text{301–400 miles}& \text{12}& \text{14}& \text{21}& \text{47}\\ \text{401–500 miles}& \text{6}& \text{6}& \text{10}& \text{22}\\ \text{Total}& \text{73}& \text{67}& \text{60}& \text{200}\end{array}$$

How many passengers are expected to travel between 401 and 500 miles and purchase first-class tickets?

OpenStax, Statistics · §11.3 Test of Independence · Exercise 7