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 o customers responding to a promotion of 200 customers, 103 applied for Silver, 59 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 r2 statistic. c) How many degrees of freedom does the 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 nmber of platinum card customers is (Type an integer or a decimal.) b)2(Round to three decimal places as needed.) c Type an integer or a decimal.)

Explanation / Answer

Ans:

a)Expected number of Silver cards customers=200*0.6=120

Expected number of Gold cards customers=200*0.3=60

Expected number of Platinum cards customers=200*0.1=20

b)Test statistic=18.625

c)df=3-1=2

card Observed(O) Expected(E) (O-E)^2/E Silver 103 120 2.408 Gold 59 60 0.017 Platinum 38 20 16.200 Total 200 200 18.625

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