At a major credit card bank, the percentages of people who historically apply for the Silver, Gold and Platinum cards are 60 %, 30 % and 10 %10 respectively. In a recent sample of customers responding to a promotion, of 200 customers,111 applied for Silver, 51 for Gold and 38 for Platinum. Is there evidence to suggest that the percentages for this promotion may be different from the historical proportions?

a) What is the expected number of customers applying for each type of card in this sample if the historical proportions are still true?

b) Compute the χ2 statistic.

c) How many degrees of freedom does the χ2 statistic have?