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 71 127 Age 30 to 34 years 75 145 Age 35 to 39 years 70 142 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 (homogeneity/ independence) would be the appropriate test, because individuals in (a simple sample/ each of two or more independent samples) are classified according to (a single categorical variable/ 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 ? = 0.05. State the appropriate null and alternative hypotheses. H0: There is no association between whether or not people pay their balance in full each month and age. Ha: There is an association between whether or not people pay their balance in full each month and age. H0: There is an association between whether or not people pay their balance in full each month and age. Ha: There is no 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. Ha: 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: The proportions of people who do and do not pay their balance in full each month are not the same for all age groups. Ha: The proportions of people who do and do not pay their balance in full each month are the same for all age groups. X^2=_______? 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 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. (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 all Americans. 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 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 who have at least one credit card.

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 71 127 Age 30 to 34 years 75 145 Age 35 to 39 years 70 142 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 (homogeneity/ independence) would be the appropriate test, because individuals in (a simple sample/ each of two or more independent samples) are classified according to (a single categorical variable/ 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 ? = 0.05. State the appropriate null and alternative hypotheses. H0: There is no association between whether or not people pay their balance in full each month and age. Ha: There is an association between whether or not people pay their balance in full each month and age. H0: There is an association between whether or not people pay their balance in full each month and age. Ha: There is no 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. Ha: 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: The proportions of people who do and do not pay their balance in full each month are not the same for all age groups. Ha: The proportions of people who do and do not pay their balance in full each month are the same for all age groups. X^2=_? 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 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. (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 all Americans. 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 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 who have at least one credit card.

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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	Pay Full Balance Each Month	Carry Balance from Month to Month
Age 20 to 24 years	75	95
Age 25 to 29 years	71	127
Age 30 to 34 years	75	145
Age 35 to 39 years	70	142

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 (homogeneity/ independence) would be the appropriate test, because individuals in (a simple sample/ each of two or more independent samples) are classified according to (a single categorical variable/ 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 ? = 0.05.

State the appropriate null and alternative hypotheses.

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: 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.

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: 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.

X^2=_______?

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 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.

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

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 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 who have at least one credit card.

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