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 study of customers responding to a promotion, of 200 customers, 110 applied for Silver, 55 for Gold and 35 for Platinum. The observed and expected data are summarised in the table below: Card Type Observed Expected (O-E)/E Silver 110 120 0.833 Gold Platinum 35 20 11.250 Use the output and your calculator to answer questions 1-3. 1. What is the expected value for Gold card applicants? (integer) 2. What is the contribution to chi-squared for Gold card applicants? (3 dp) 3. What is the chi-squared test statistic? (2 dp) 4. Using Excel, determine the p-value: (4 dp) 5. Would you (A) reject or (B) not reject the hypothesis that the proportions are as stated?

Answer 1

Chi square test for Goodness of fit

expected frequncy,E = expected proportions*total frequency

total frequency=200

category	observed frequencey, O	expected proportion	expected frequency,E			(O-E)²/E
silver	110	0.60	120.00			0.833
gold	55	0.30	60.00			0.417
platinum	35	0.10	20.00			11.250

1)

gold expected value = 200*0.30 = 60

2)

contribution = 0.417

3)

chi square test statistic,X² = Σ(O-E)²/E =12.500

4)

Degree of freedom=k-1=3-1=2

  

P value =0.0019                                [ excel function: =chisq.dist.rt(test-stat,df) ]

5)

Decision: P value < α,          Reject Ho

answer : A