A recent study of undergraduates looked at gender differences in dieting trends.
ID: 3170116 • Letter: A
Question
A recent study of undergraduates looked at gender differences in dieting trends. There were 188 women and 101 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender:
(a) Fill in the missing cells of the table.
(b) Summarize the data numerically. What percent of each gender has tried low-fat diets? (Round your answers to two decimal places.)
(c) Test that there is no association between gender and the likelihood of trying a low-fat diet. (Round your 2 to three decimal places, and round your P-value to four decimal places.)
Explanation / Answer
Solution:
Part a
Fill in the missing cells
Tried
Women
Men
Total
Yes
38
8
46
No
150
93
243
Total
188
101
289
Part b
Percentage of women = 188/289 = 0.650519 or 65.05%
Percentage of men = 101/289 = 0.349481 = 34.95%
Part c
Here, we have to test whether there is any association between gender and the likelihood of trying a low fat diet. The null and alternative hypotheses are given as below:
Null hypothesis: H0: There is no any association between gender and likelihood of trying a low fat diet.
Alternative hypothesis: Ha: There is an association between gender and likelihood of trying a low fat diet.
We assume a 5% level of significance for this test.
The test statistic formula is given as below:
Chi square = [(O – E)^2/E]
Where, O = observed frequencies and E = Expected frequencies
E = (Row total * Column total) / Grand total
The calculation tables and test statistic is given as below:
Chi-Square Test
Observed Frequencies
Gender
Tried low fat diet
Women
Men
Total
Yes
38
8
46
No
150
93
243
Total
188
101
289
Calculations
(O – E)
8.076125
-8.07612
-8.07612
8.076125
Expected Frequencies
Gender
Tried low fat diet
Women
Men
Total
Yes
29.92388
16.07612
46
No
158.0761
84.92388
243
Total
188
101
289
(O – E)^2/E
2.179657
4.057184
0.41261
0.768027
Number of rows = r = 2
Number of columns = c = 2
Degrees of freedom = (r – 1)(c – 1) = (2 – 1)(2 – 1) = 1*1 = 1
Data
Level of Significance
0.05
Number of Rows
2
Number of Columns
2
Degrees of Freedom
1
Results
Critical Value
3.841459
Chi-Square Test Statistic
7.417477
p-Value
0.006459
Reject the null hypothesis
We reject the null hypothesis that there is no any association between gender and likelihood of trying a low fat diet.
We conclude that there is an association between gender and likelihood of trying a low fat diet.
Tried
Women
Men
Total
Yes
38
8
46
No
150
93
243
Total
188
101
289