14.59 A manufacturer of household appliances wanted to determine if there was a relationship between family size and the size of washing machines purchased by customers. The manufacturer was preparing guidelines for sales personnel and wanted to know if the sales staff should make specific recommendations to customers.

A random sample of 300 families was asked about their family size and size of the washing machine they owned.

For the 40 families with one or two people, 25 had an 8-pound washer, 10 had a 10-pound washer, and 5 had a 12-pound washer. The 140 families with three or four people included 37 with the 8-pound washer, 62 with the 10-pound washer, and 41 with the 12-pound washer. For the remaining 120 families with five or more people, 8 had an 8-pound washer, 53 had a 10-pound washer, and 59 had a 12-pound washer. Based on these results, what can be concluded about family size and size of washer? Construct a two-way table, state the hypothesis, compute the statistics, and state your conclusion.