CAIE FP2 2013 November — Question 10

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2013
SessionNovember
TopicChi-squared distribution

10 Customers were asked which of three brands of coffee, \(A , B\) and \(C\), they prefer. For a random sample of 80 male customers and 60 female customers, the numbers preferring each brand are shown in the following table.
\(A\)\(B\)\(C\)
Male323612
Female183012
Test, at the \(5 \%\) significance level, whether there is a difference between coffee preferences of male and female customers. A larger random sample is now taken. It consists of \(80 n\) male customers and \(60 n\) female customers, where \(n\) is a positive integer. It is found that the proportions choosing each brand are identical to those in the smaller sample. Find the least value of \(n\) that would lead to a different conclusion for the 5\% significance level hypothesis test.