Question

9-37. Many banks and other financial institutions have raised the minimum payment customers must pay on their outstanding credit card balances.

Suppose a claim is made that more than 40% of all credit card holders pay the minimum payment. To test this claim, a random sample of payments made by credit card customers was collected.

The sample contained data for 400 customers, of which 174 paid the minimum payment.

a. State the appropriate null and alternative hypothesis.

b. Based on the sample data, test the null hypothesis using an alpha level equal to 0.05. Discuss the results of the test.

Answer 1

Solution :

Given that,

Point estimate = sample proportion = = x / n = 0.435

This a right (One) tailed test.

The null and alternative hypothesis is,

Ho: p = 0.40

Ha: p 0.40

Test statistics

z = ( - ) / *(1-) / n

= ( 0.435 - 0.40) / (0.40*0.60) / 400

= 1.43

P-value = P(Z > z )

= 1 - P(Z < 1.43 .)

= 1 - 0.9236

= 0.0764

The p-value is p = 0.0764, and since p = 0.0764 > 0.05, it is concluded that the null hypothesis is not rejected.