For the customers in Exercise,
In exercise 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, 110 applied for Silver, 55 for Gold, and 35 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 x2 statistic to be (what is the mean of the x2 distribution)?
b) Does the statistic you computed in Exercise 2 seem large in comparison to this mean? Explain briefly.
c) What does that say about the null hypothesis?
d) Find the α = 0.05 critical value for the x2 distribution with the appropriate number of df.
e) Using the critical value, what do you conclude about the null hypothesis at α = 0.05?