Question

There is a popular story (among data miners) that there is a correlation between men buying diapers and buying beer while shopping. A student tests this theory by surveying 133 male shoppers as they left a grocery store. The results are summarized in the contingency table. Test for a dependent relationship between buying beer and buying diapers. Conduct this test at the 0.01 significance level.

	Bought Diapers	Did Not Buy Diapers	Totals
Beer	9	51	60
No Beer	11	62	73
Totals	20	113	133

(a) Find the expected frequencies.

(b) Find the test statistic

(c) Find the critical value

is this correct?

a.

Expected value	Bought diapers	Did not buy diapers	Total
Beer	9.02	50.98	60.00
No beer	10.98	62.02	73.00
Total	20.00	113.00	133.00

b. 0

c. 6.635

is this all correct?

Answer 1

Yes all of them are correct: below is working

a)below is expected frequency table:

Expected	Ei=row total*column total/grand total	Bought	did not	Total
	Beer	9.02	50.98	60
	No Beer	10.98	62.02	73
	total	20	113	133

b)

Applying chi square test of independence:

chi square    χ2	=(Oi-Ei)2/Ei	Bought	did not	Total
	Beer	0.000	0.000	0.0001
	No Beer	0.000	0.000	0.0001
	total	0.0001	0.0000	0.0001
test statistic X2 =		0.0001

c)

degree of freedom(df) =(rows-1)*(columns-1)=		1
for 1 df and 0.01 level , critical value       χ2=		6.635
Decision rule : reject Ho if value of test statistic X2>6.635