Question

A recent study of undergraduates looked at gender differences in dieting trends. There were 182 women and 108 men who participated in the survey. The table below summarizes whether a student tried a low-fat diet or not by gender:

		Gender
Tried low-fat diet		Women		Men
Yes		36		9
No

(a) Fill in the missing cells of the table.

		Gender
Tried low-fat diet		Women		Men
Yes		36		9
No

(b) Summarize the data numerically. What percent of each gender has tried low-fat diets? (Round your answers to two decimal places.)

women	%
men	%

(c) Test that there is no association between gender and the likelihood of trying a low-fat diet. (Round your χ² to three decimal places, and round your P-value to four decimal places.)

χ2	=
df	=
P-value	=

Summarize the results.

There is strong evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.There is no evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.     

Answer 1

a)

Oi	Women	Men
Yes	36	9
No	146	99

b)

women	19.78%
men	8.33%

c)Applying chi square test:

Expected	Ei=row total*column total/grand total	Women	Men	Total
	Yes	28.24	16.76	45
	No	153.76	91.24	245
	total	182	108	290
chi square    χ2	=(Oi-Ei)2/Ei	Women	Men	Total
	Yes	2.1315	3.5920	5.723
	No	0.3915	0.6597	1.051
	total	2.523	4.252	6.775

X² =6.775

df =1

p value =0.0092

There is strong evidence at the 5% level that gender and the likelihood of trying a low-fat diet are related.