Beer and Diapers: There is a popular story(among data miners) that there is a correlation between men buyingdiapers and buying beer while shopping. A student tests this theoryby surveying 160 male shoppers as they left a grocery store. Theresults are summarized in the contingency table below.

Observed Frequencies: O_i's

	Bought Â	  DidNot Â
	  Diapers Â	  BuyDiapers Â	  Totals Â
Beer Â	  8 Â	  21 Â	  29 Â
No Beer Â	  10 Â	  121 Â	  131 Â
Totals Â	  18 Â	  142 Â	  160 Â

The Test: Test for a dependent relationshipbetween buying beer and buying diapers. Conduct this test at the0.01 significance level.

(a) What is the test statistic? Round your answer to 3decimal places.

χ²

=

(b) What is the conclusion regarding the null hypothesis?

reject H₀fail to rejectH₀    

(c) Choose the appropriate concluding statement.

The evidence suggests that all men who buy diapers also buybeer.The evidence suggests that the probability of a man buyingbeer is dependent upon whether or not he buysdiapers.     There is not enough evidenceto conclude that the probability of a man buying beer is dependentupon whether or not he buys diapers.We have proven that buying beerand buying diapers are independent variables.