At a major credit card bank the percentages of people who hi

At a major credit card bank, the percentages of people who historically apply for silver, gold and platinum cards are 60%, 30% and 10% respectively. In a recent sample of customers responding to a promotion, of 200 customers, 137 applied for silver, 50 for gold and 13 for platinum. Is there evidence to suggest that the percentages for this promotion may be different from the historical proportions?

a. If the customers apply for the three cards according to the historical proportions, about how big, on average, would you expect the x^2 statistic to be (what is the mean of the x^2 distribution)?

b. The computed x^2 statistic for the given data is 6.525. Does this seem large in comparison to the mean in part a?

c. Find the a= 0.05 critical value for the x^2 distribution with the appropriate number of df.

Solution

At a major credit card bank, the percentages of people who historically apply for silver, gold and platinum cards are 60%, 30% and 10% respectively. In a recent sample of customers responding to a promotion, of 200 customers, 137 applied for silver, 50 for gold and 13 for platinum. Is there evidence to suggest that the percentages for this promotion may be different from the historical proportions?

DF =number of categories -1= 3-1=2

mean of the x^2 distribution = DF=2

b. The computed x^2 statistic for the given data is 6.525. Does this seem large in comparison to the mean in part a?

computed value =6.525   > 2.

Computed value large in comparison to the mean of the distribution.

c. Find the a= 0.05 critical value for the x^2 distribution with the appropriate number of df.

DF =3-1=2

critical value =5.991