At a major credit card bank, the percentages of people who historically apply fo

Question

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% respectively. In a recent sample of customers responding to a promotion, of 200 customers. 111 applied for Silver, 61 for Gold and 28 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 chi _2 statistic. c) How many degrees of freedom does the chi _2 statistic have? a) The expected number of silver card customers is. (Type an integer or a decimal.) The expected number of gold card customers is. (Type an integer or a decimal.) The expected number of platinum card customers is. (Type an integer or a decimal.) b) chi _3 = (Round to three decimal places as needed.) c) df = (Type an integer or a decimal.)

Explanation / Answer

a) expected number of silver card customer =200*0.6=120

expected number of gold card customer =200*0.3=60

expected number of platinum card customer =200*0.1=20

b) applying chi square goodness of fit test:

X2 =3.892

d) df =n-1=3-1=2

observed Expected Chi square cents portion Probability O E=total*p =(O-E)^2/E silver 0.600 111.000 120.00 0.68 gold 0.300 61.000 60.00 0.02 platinum 0.100 28.000 20.00 3.20 1 200 200 3.8917

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