1. Does our data provide significant evidence that Gold card holders are more likely to pay off their cards in full each month than other types of credit card holders?

a. Write out the null and alternative hypothesis using correct notation.

b. Calculate the value of the test statistic and use this to make the decision of the test. Show your working.

c. Interpret your results in the context of the question.

d. Show that the necessary conditions hold for this test to be valid

e. Given your decision, what type of error could you have possibly made?

2. Does our data provide sufficient evidence that Credit Card Balances for Single Female Gold Card holders are less than the Credit Card Balances for Single Male Gold Card holders?

a. Why do we need to use a non-parametric test to answer the above question?

b. State the null and alternative hypotheses being tested by the non-parametric test, in context.

c. From the appropriate SPSS output, state the value of the standardised test statistic and use the p-value to

make the decision of the test. (Use ? = 0.05)

d. Interpret your result in context.

Simple Histogram of Income by Cardholders 60 40 Single Male Frequency Percent 20 0 Cardholders 60 40 Single Female Frequency Percent 20 0 $0 $20,000 $40,000 $60,000 $80,000 $100,000 $120,000 IncomePayment * GoldCard Crosstabulation GoldCard Gold Other Types Total Payment Minimum Count 145 149 % within GoldCard 5.1% 18.8% 17.5% Other Count 32 334 366 % within GoldCard 41.0% 43.3% 43.1% Full Balance Count 42 293 335 % within GoldCard 53.8% 38.0% 39.4% Total Count 78 772 850 % within GoldCard 100.0% 100.0% 100.0%Balance Standard Mean Count Median Deviation Cardholders Single Male $2,849 54 $2,735 $829 Single Female $2,364 8 $2,300 $309Hypothesis Test Summary Null Hypothesis Test Sig. a.b Decision The medians of Balance are the Independent-Samples Median 0720 Retain the null hypothesis. same across categories of Test Cardholders. 2 The distribution of Balance is the Independent-Samples Mann- 059 Retain the null hypothesis. same across categories of Whitney U Test Cardholders. a. The significance level is .050. b. Asymptotic significance is displayed.Independent-Samples Median Test Summary a. ore than 20% ofthe cells have expected values less than five. b. Multiple comparisons are not performed because the overall test does not show signicant differences across samples. Independent-Samples Mann-Whitney U Test Cardholders Single Female Single Male $6,000 N = 8 Single Male $6,000 Mean Rank = 20.25 $5,000 $5,000 $4,000 $4,000 $3,000 $3,000 Balance Balance $2,000 $2,000 $1,000 $1,000 $0 $0 12 10 8 6 4 2 0 2 4 6 8 10 12 Frequency Frequency