Because of the current concern over credit card balances, a bank’s chief financial officer is interested in whether there is a relationship between account balances and the number of times a card is used each month. A random sample of 50 accounts was selected. The account balance and the number of charges during the past month were the two variables recorded. The correlation coefficient for the two variables was - 0.23.
a. Discuss what the r = - 0.23 measures. Make sure to frame your discussion in terms of the two variables mentioned here.
b. Using an α = 0.10 level, test to determine whether there is a significant linear relationship between account balance and the number of card uses during the past month. State the null and alternative hypotheses and show the decision rule.
c. Consider the decision you reached in part b. Describe the type of error you could have made in the context of this problem.