Beer and Diapers: There is a popular story (among data miners) that there is a c

Question

Beer and Diapers: 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 140 male shoppers as they left a grocery store. The results are summarized in the contingency table below.

Observed Frequencies: Oi's

The Test: Test for a dependent relationship between buying beer and buying diapers. Conduct this test at the 0.05 significance level.

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

2

=  

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

reject H0fail to reject H0    

(c) Choose the appropriate concluding statement.

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

Bought     Did Not     Diapers     Buy Diapers     Totals   Beer     7     44     51   No Beer     8     81     89   Totals     15     125     140  

Explanation / Answer

Ans:

H0:buying beer and buying diaper are independent.

H1:buying beer and buying diaper are not independent.

Expected count=row total*column total/overall total

p-value=CHIDIST(0.76,1)=0.3833

As,p-value>0.05,we fail to reject null hypothesis,H0.

We have sufficient evidence to conclude that buying beer and buying diaper are independent.

There is not enough evidence to conclude that the probability of a man buying beer is dependent upon whether or not he buys diapers.We have proven that buying beer and buying diapers are independent variables.

Observed(O) Bought     Did Not     Diapers     Buy Diapers     Totals   Beer   7 44 51 No Beer   8 81 89 Totals   15 125 140 Expected(E) Bought     Did Not     Diapers     Buy Diapers     Totals   Beer   5.46 45.54 51 No Beer   9.54 79.46 89 Totals   15 125 140 Chi square=(O-E)^2/E 0.432 0.052 0.247 0.030 Total Chi square score=0.760

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