12.32 The following passage is from the paper “Gender Differences in Food Selections of Students at a Historically Black College and University” (College Student Journal

[2009]: 800–806):

Also significant was the proportion of males and their water consumption (8 oz. servings)

compared to females (X 2 5 8.16, P 5 .086).

Males came closest to meeting recommended daily water intake (64 oz. or more) than females

(29.8% vs. 20.9%).

This statement was based on carrying out a X 2 test of independence using data in a two-way table where rows corresponded to gender (male, female) and columns corresponded to number of servings of water consumed per day, with categories none, one, two to three, four to five, and six or more.

a. What hypotheses did the researchers test? What is the number of degrees of freedom associated with the report value of the X 2 statistic?

b. The researchers based their statement that the proportions falling in the water consumption categories were not all the same for males and females on a test with a significance level of .10.

Would they have reached the same conclusion if a significance level of .05 had been used? Explain.

c. The paper also included the accompanying data on how often students said they had consumed fried potatoes (fries or potato chips) in the past week.

Number of Times Consumed Fried Potatoes in the Past Week 0 1 to 3 4 to 6 7 to 13 14 to 20 21 or more Gender Male 2 10 15 12 6 3 Female 15 15 10 20 19 12 Use the Minitab output that follows to carry out a X 2 test of independence. Do you agree with the authors’ conclusion that there was a significant association between gender and consumption of fried potatoes?

Expected counts are printed below observed counts Chi-Square contributions are printed below expected counts 0 1-3 4-6 7-13 14-20 21 or more Total M 2 10 15 12 6 3 48 5.87 8.63 8.63 11.05 8.63 5.18 2.552 0.216 4.696 0.082 0.803 0.917 F 15 15 10 20 19 12 91 11.13 16.37 16.37 20.95 16.37 9.82 1.346 0.114 2.477 0.043 0.424 0.484 Total 17 25 25 32 25 15 139 Chi-Sq 5 14.153, DF 5 5, P-Value 5 0.015