Question

A recent study of undergraduates looked at gender differences in dieting trends. There were 182 women and 105 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 37 9

No

(a) Fill in the missing cells of the table. Gender Tried low-fat diet

Women Men

Yes 37 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)

	Women	Men	total
Yes	37	9	46
No	182-37=145	105-9=96	241
total	182	105	287

(b)

women %=100*37/182=20.33

men %=100*9/105=8.57

(c) here we use chi-square test with

null hypothesis H0: there is no association between gender and trying low fat diet

alternate hypothesis Ha: there is association between gender and trying low fat diet

the test statistics is given as

χ2 =6.84

df =1

P-value =0.0089

chi-square =sum((O-E)²/E)=6.84 with df= (r-1)(c-1)=(2-1)(2-1)=1

p-value=P(χ2>6.84)

since p-value is less than typical level of significance alpha=0.05, so we reject null hypothesis

so right choice is

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

follwoing information has been generated for answering above

	observed(O)	Expected(E)	E	(O-E)	(O-E)2/E
	37	46*182/287	29.17	7.83	2.10
	9	46*105/287	16.83	-7.83	3.64
	145	241*182/287	152.83	-7.83	0.40
	96	241*105/287	88.17	7.83	0.70
sum=	287	0	287	-1.42E-14	6.84