CAIE FP2 2012 June — Question 10

Exam BoardCAIE
ModuleFP2 (Further Pure Mathematics 2)
Year2012
SessionJune
TopicChi-squared distribution

10 Random samples of employees are taken from two companies, \(A\) and \(B\). Each employee is asked which of three types of coffee (Cappuccino, Latte, Ground) they prefer. The results are shown in the following table.
CappuccinoLatteGround
Company \(A\)605232
Company \(B\)354031
Test, at the 5\% significance level, whether coffee preferences of employees are independent of their company. Larger random samples, consisting of \(N\) times as many employees from each company, are taken. In each company, the proportions of employees preferring the three types of coffee remain unchanged. Find the least possible value of \(N\) that would lead to the conclusion, at the \(1 \%\) significance level, that coffee preferences of employees are not independent of their company.