Question

A report describes a study conducted by a bank. Data consistent with summary values given in the report are summarized in the table. Suppose that this data resulted from a random sample of 800 adult Americans age 20 to 39 years old who have at least one credit card. Each person in the sample was classified according to age (with possible categories of 20 to 24 years, 25 to 29 years, 30 to 34 years, and 35 to 39 years). The people in the sample were also classified according to whether or not they pay the full balance on their credit cards each month or sometimes or always carry over a balance from month to month.

	Pay Full Balance Each Month	Carry Balance from Month to Month
Age 20 to 24 years	75	95
Age 25 to 29 years	73	128
Age 30 to 34 years	75	145
Age 35 to 39 years	68	141

(a) To investigate whether or not people paying their balance in full each month is related to age, which chi-square test (homogeneity or independence) would be the appropriate test? Explain your choice.

A chi-square test of  ---Select--- homogeneity or independence would be the appropriate test, because individuals in  ---Select--- a single sample or each of two or more independent samples are classified according to  ---Select--- a single categorical variable or two categorical variables .

(b) Carry out an appropriate test to determine if these data provide convincing evidence that whether or not people pay their balance in full each month is related to age. Use α = 0.05.

State the appropriate null and alternative hypotheses.

H₀: The proportions of people who do and do not pay their balance in full each month are not the same for all age groups.
H_a: The proportions of people who do and do not pay their balance in full each month are the same for all age groups.

H₀: There is no association between whether or not people pay their balance in full each month and age.
H_a: There is an association between whether or not people pay their balance in full each month and age.  

H₀: The proportions of people who do and do not pay their balance in full each month are the same for all age groups.
H_a: The proportions of people who do and do not pay their balance in full each month are not the same for all age groups.

H₀: There is an association between whether or not people pay their balance in full each month and age.
H_a: There is no association between whether or not people pay their balance in full each month and age.

Find the test statistic and P-value. (Use technology. Round your test statistic to three decimal places and your P-value to four decimal places.)

X²=

P-value=

State the conclusion in the problem context.

Fail to reject H₀. There is convincing evidence to conclude that whether or not people pay their balance in full each month is related to age.

Reject H₀. There is not convincing evidence to conclude that whether or not people pay their balance in full each month is related to age.

Fail to reject H₀. There is not convincing evidence to conclude that whether or not people pay their balance in full each month is related to age.

Reject H₀. There is convincing evidence to conclude that whether or not people pay their balance in full each month is related to age.

(c) To what population would it be reasonable to generalize the conclusion from the test in part (b)?

It would be reasonable to generalize this conclusion to the population of adult Americans age 20 to 39 years old who have at least one credit card.

It would be reasonable to generalize this conclusion to the population of adult Americans age 20 to 39 years old.

It would be reasonable to generalize this conclusion to the population of all Americans who have at least one credit card.

It would be reasonable to generalize this conclusion to the population of adult Americans age 20 to 39 years old who do not have a credit card.

It would be reasonable to generalize this conclusion to the population of all Americans.

Answer 1

The statistical software output for this problem is:

Hence,

a) Independence; a single sample; two categorical variables

b) H₀: There is no association between whether or not people pay their balance in full each month and age.
H_a: There is an association between whether or not people pay their balance in full each month and age.

Option B is correct.

Test statistic = 6.231

P-value = 0.1009

Conclusion: Fail to reject H₀. There is not convincing evidence to conclude that whether or not people pay their balance in full each month is related to age. Option C is correct.

c) It would be reasonable to generalize this conclusion to the population of adult Americans age 20 to 39 years old who have at least one credit card. Option A is correct.