Researchers at the University of Nebraska carried out a study on gender differen
ID: 3201749 • Letter: R
Question
Researchers at the University of Nebraska carried out a study on gender differences in dieting trends among a group of midwestern college students. Students were recruited from an introductory nutrition course during one term. There were 286 participants in the study, 105 men and 171 women. Of the 171 women, 35 had tried a low fat diet, and 146 had not tried a low fat diet. Among the 105 men, 8 had tried a low fat diet and 97 had not tried a low fat diet.
a. Write down the appropriate hypothesis test to see if there is a relationship between gender and diet
b. Can the results from such a test be generalized to the entire population of midwestern college students? Why or why not?
Explanation / Answer
a.
H0: There is no relationship
H1: There is relationship
Here we are going to use chi-square test of independence:
c^2 = S [ (Oi – Ei)^2 / Ei ]
Oi = Observed values
Ei = Expected values
Ei = ( row total *column total ) / Total
Oi
Lot fat
Not low fat
Total
Men
8
97
105
Women
35
146
181
Total
43
243
286
Ei
(43 * 105 ) / 286 = 15.7876
Lot fat
Not low fat
Total
Men
15.7867
89.2133
105
Women
27.2133
153.7867
181
Total
43
243
286
Oi – Ei
Lot fat
Not low fat
Men
-7.7867
7.7867
Women
7.7867
-7.7867
(Oi – Ei)^2
Lot fat
Not low fat
Men
60.633
60.633
Women
60.633
60.633
(Oi-Ei)^2/Ei
Lot fat
Not low fat
Total
Men
3.84
0.68
4.52
Women
2.23
0.39
2.62
c^2 = S [ (Oi – Ei)^2 / Ei ]
= 4.52 + 2.62 = 7.14
The critical value is 3.841 for 1 degrees of freedom at 5% level of significance.
The test value is greater than the critical value (7.14>3.841). We reject the null hypothesis and we can conclude that there is a relationship between gender and diet.
b.
No. The result from such a test cannot be generalized to the entire population of Midwestern college students as the students were recruited only from an introductory nutrition course during one term.
Lot fat
Not low fat
Total
Men
8
97
105
Women
35
146
181
Total
43
243
286
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