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.

	bought diapers	did not buy diapers
beer
no beer

b. find the test statistic

c. find the critical value

d. sufficient data to support claim?

Answer 1

Ho: The two variables men buying diapers and buying beer while shopping are independent.

Ha: The two variables men buying diapers and buying beer while shopping are not independent.  

(a) Expected frequencies = (row total * coloumn total) / grand total

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) test statistics

Squared distances	Bought diapers	Did not buy diapers	Total
Beer	0.000	0.000	0.000
No beer	0.000	0.000	0.000
Total	0.000	0.000	0.000

= 0

(d) critical at level of significance 0.01 = 6.635

As (0) is less than critical, we fail to reject the Null hypothesis.

Hence we do not have sufficient evidence to believe that  men buying diapers and buying beer while shopping are not independent.