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 136 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	5	52	57
No Beer	7	72	79
Totals	12	124	136

(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) Is there sufficient data to support the claim?
Yes
No

Answer 1

a)

expected value formula

	Bought Diapers	Did Not Buy Diapers
Beer	5.029	21.971
No Beer	6.971	72.029

b)

Chi-square Test
Σ (Observed - Expected) ^ 2 / Expected
	Therapy 1	Therapy 2	Total
Cured	0.000172	1.66E-05	0.000189
Not Cured	0.000124	1.2E-05	0.000136
		χ2 =	0.000325

c)

α	0.01
df	(r-1)*(c-1)=1
χ2	0.000325
p-value	0.985622
χ2-crit	6.634897
sig	no

d)

No