For Problems 1 and 2, (a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, (c) explain what it would mean to make a Type II error, (d) state the conclusion that would be reached if the null hypothesis is not rejected , and (e) state the conclusion that would be reached if the null hypothesis is rejected . 1. Credit-Card Debt According to creditcard.com , the mean outstanding credit-card debt of college undergraduates was $3173 in 2010. A researcher believes that this amount has decreased since then.

Question

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Answer 1

Textbook Question

Chapter 10, Problem 1RE

For Problems 1 and 2, (a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, (c) explain what it would mean to make a Type II error, (d) state the conclusion that would be reached if the null hypothesis is not rejected, and (e) state the conclusion that would be reached if the null hypothesis is rejected.

1. Credit-Card Debt According to creditcard.com, the mean outstanding credit-card debt of college undergraduates was $3173 in 2010. A researcher believes that this amount has decreased since then.

a.

Expert Solution

To determine

The null and alternative hypotheses.

Answer to Problem 1RE

Null hypothesis:

H0:μ=$3,173_ .

Alternative hypothesis:

H1:μ<$3,173_ .

Explanation of Solution

Given info:

In 2010, a researcher believed that the mean credit card debt of college graduates has been decreased.

Justification:

Null hypothesis:

H0:μ=$3173

That is, the mean outstanding credit card debt of college graduates has not been decreased since 2010.

Alternative hypothesis:

H1:μ<$3173

That is, the mean outstanding credit card debt of college graduates has been decreased since 2010.

b.

Expert Solution

To determine

The occurrence of type-I error.

Explanation of Solution

Type I error: Rejecting the null hypothesis, when it is actually true.

A type-I error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has not been decreased since 2010.

c.

Expert Solution

To determine

The occurrence of type-II error.

Explanation of Solution

Type II error: Fail to reject the null hypothesis, when it is false.

A type-II error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has not been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has been decreased since 2010.

d.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is no sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010”.

Explanation of Solution

Conclusion:

From the given information, the null hypothesis is not rejected. Thus, there is no enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

e.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Explanation of Solution

From the given information, the null hypothesis is rejected. Thus, there is enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

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Answer 2

Textbook Question

Chapter 10, Problem 1RE

For Problems 1 and 2, (a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, (c) explain what it would mean to make a Type II error, (d) state the conclusion that would be reached if the null hypothesis is not rejected, and (e) state the conclusion that would be reached if the null hypothesis is rejected.

1. Credit-Card Debt According to creditcard.com, the mean outstanding credit-card debt of college undergraduates was $3173 in 2010. A researcher believes that this amount has decreased since then.

a.

Expert Solution

To determine

The null and alternative hypotheses.

Answer to Problem 1RE

Null hypothesis:

H0:μ=$3,173_ .

Alternative hypothesis:

H1:μ<$3,173_ .

Explanation of Solution

Given info:

In 2010, a researcher believed that the mean credit card debt of college graduates has been decreased.

Justification:

Null hypothesis:

H0:μ=$3173

That is, the mean outstanding credit card debt of college graduates has not been decreased since 2010.

Alternative hypothesis:

H1:μ<$3173

That is, the mean outstanding credit card debt of college graduates has been decreased since 2010.

b.

Expert Solution

To determine

The occurrence of type-I error.

Explanation of Solution

Type I error: Rejecting the null hypothesis, when it is actually true.

A type-I error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has not been decreased since 2010.

c.

Expert Solution

To determine

The occurrence of type-II error.

Explanation of Solution

Type II error: Fail to reject the null hypothesis, when it is false.

A type-II error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has not been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has been decreased since 2010.

d.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is no sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010”.

Explanation of Solution

Conclusion:

From the given information, the null hypothesis is not rejected. Thus, there is no enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

e.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Explanation of Solution

From the given information, the null hypothesis is rejected. Thus, there is enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

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Answer 3

Textbook Question

Chapter 10, Problem 1RE

For Problems 1 and 2, (a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, (c) explain what it would mean to make a Type II error, (d) state the conclusion that would be reached if the null hypothesis is not rejected, and (e) state the conclusion that would be reached if the null hypothesis is rejected.

1. Credit-Card Debt According to creditcard.com, the mean outstanding credit-card debt of college undergraduates was $3173 in 2010. A researcher believes that this amount has decreased since then.

a.

Expert Solution

To determine

The null and alternative hypotheses.

Answer to Problem 1RE

Null hypothesis:

H0:μ=$3,173_ .

Alternative hypothesis:

H1:μ<$3,173_ .

Explanation of Solution

Given info:

In 2010, a researcher believed that the mean credit card debt of college graduates has been decreased.

Justification:

Null hypothesis:

H0:μ=$3173

That is, the mean outstanding credit card debt of college graduates has not been decreased since 2010.

Alternative hypothesis:

H1:μ<$3173

That is, the mean outstanding credit card debt of college graduates has been decreased since 2010.

b.

Expert Solution

To determine

The occurrence of type-I error.

Explanation of Solution

Type I error: Rejecting the null hypothesis, when it is actually true.

A type-I error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has not been decreased since 2010.

c.

Expert Solution

To determine

The occurrence of type-II error.

Explanation of Solution

Type II error: Fail to reject the null hypothesis, when it is false.

A type-II error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has not been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has been decreased since 2010.

d.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is no sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010”.

Explanation of Solution

Conclusion:

From the given information, the null hypothesis is not rejected. Thus, there is no enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

e.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Explanation of Solution

From the given information, the null hypothesis is rejected. Thus, there is enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

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Answer 4

Textbook Question

Chapter 10, Problem 1RE

For Problems 1 and 2, (a) determine the null and alternative hypotheses, (b) explain what it would mean to make a Type I error, (c) explain what it would mean to make a Type II error, (d) state the conclusion that would be reached if the null hypothesis is not rejected, and (e) state the conclusion that would be reached if the null hypothesis is rejected.

1. Credit-Card Debt According to creditcard.com, the mean outstanding credit-card debt of college undergraduates was $3173 in 2010. A researcher believes that this amount has decreased since then.

a.

Expert Solution

To determine

The null and alternative hypotheses.

Answer to Problem 1RE

Null hypothesis:

H0:μ=$3,173_ .

Alternative hypothesis:

H1:μ<$3,173_ .

Explanation of Solution

Given info:

In 2010, a researcher believed that the mean credit card debt of college graduates has been decreased.

Justification:

Null hypothesis:

H0:μ=$3173

That is, the mean outstanding credit card debt of college graduates has not been decreased since 2010.

Alternative hypothesis:

H1:μ<$3173

That is, the mean outstanding credit card debt of college graduates has been decreased since 2010.

b.

Expert Solution

To determine

The occurrence of type-I error.

Explanation of Solution

Type I error: Rejecting the null hypothesis, when it is actually true.

A type-I error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has not been decreased since 2010.

c.

Expert Solution

To determine

The occurrence of type-II error.

Explanation of Solution

Type II error: Fail to reject the null hypothesis, when it is false.

A type-II error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has not been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has been decreased since 2010.

d.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is no sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010”.

Explanation of Solution

Conclusion:

From the given information, the null hypothesis is not rejected. Thus, there is no enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

e.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Explanation of Solution

From the given information, the null hypothesis is rejected. Thus, there is enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

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Answer 5

Textbook Question

Answer 6

Textbook Question

Answer 7

a.

Expert Solution

To determine

The null and alternative hypotheses.

Answer to Problem 1RE

Null hypothesis:

H0:μ=$3,173_ .

Alternative hypothesis:

H1:μ<$3,173_ .

Explanation of Solution

Given info:

In 2010, a researcher believed that the mean credit card debt of college graduates has been decreased.

Justification:

Null hypothesis:

H0:μ=$3173

That is, the mean outstanding credit card debt of college graduates has not been decreased since 2010.

Alternative hypothesis:

H1:μ<$3173

That is, the mean outstanding credit card debt of college graduates has been decreased since 2010.

b.

Expert Solution

To determine

The occurrence of type-I error.

Explanation of Solution

Type I error: Rejecting the null hypothesis, when it is actually true.

A type-I error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has not been decreased since 2010.

c.

Expert Solution

To determine

The occurrence of type-II error.

Explanation of Solution

Type II error: Fail to reject the null hypothesis, when it is false.

A type-II error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has not been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has been decreased since 2010.

d.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is no sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010”.

Explanation of Solution

Conclusion:

From the given information, the null hypothesis is not rejected. Thus, there is no enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

e.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Explanation of Solution

From the given information, the null hypothesis is rejected. Thus, there is enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 8

a.

Expert Solution

To determine

The null and alternative hypotheses.

Answer to Problem 1RE

Null hypothesis:

H0:μ=$3,173_ .

Alternative hypothesis:

H1:μ<$3,173_ .

Explanation of Solution

Given info:

In 2010, a researcher believed that the mean credit card debt of college graduates has been decreased.

Justification:

Null hypothesis:

H0:μ=$3173

That is, the mean outstanding credit card debt of college graduates has not been decreased since 2010.

Alternative hypothesis:

H1:μ<$3173

That is, the mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

The null and alternative hypotheses.

Answer 13

Answer to Problem 1RE

Null hypothesis:

H0:μ=$3,173_ .

Alternative hypothesis:

H1:μ<$3,173_ .

Answer 14

Explanation of Solution

Given info:

In 2010, a researcher believed that the mean credit card debt of college graduates has been decreased.

Justification:

Null hypothesis:

H0:μ=$3173

That is, the mean outstanding credit card debt of college graduates has not been decreased since 2010.

Alternative hypothesis:

H1:μ<$3173

That is, the mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 15

b.

Expert Solution

To determine

The occurrence of type-I error.

Explanation of Solution

Type I error: Rejecting the null hypothesis, when it is actually true.

A type-I error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has not been decreased since 2010.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

The occurrence of type-I error.

Answer 20

Explanation of Solution

Type I error: Rejecting the null hypothesis, when it is actually true.

A type-I error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has not been decreased since 2010.

Answer 21

c.

Expert Solution

To determine

The occurrence of type-II error.

Explanation of Solution

Type II error: Fail to reject the null hypothesis, when it is false.

A type-II error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has not been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 22

c.

Expert Solution

Answer 23

c.

Expert Solution

Answer 24

Expert Solution

Answer 25

To determine

The occurrence of type-II error.

Answer 26

Explanation of Solution

Type II error: Fail to reject the null hypothesis, when it is false.

A type-II error is made by concluding the evidence as “the mean outstanding credit card debt of college graduates has not been decreased since 2010”. But in reality, the actual mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 27

d.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is no sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010”.

Explanation of Solution

Conclusion:

From the given information, the null hypothesis is not rejected. Thus, there is no enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 28

d.

Expert Solution

Answer 29

d.

Expert Solution

Answer 30

Expert Solution

Answer 31

To determine

To state: The conclusion based on the results of the test.

Answer 32

Answer to Problem 1RE

The conclusion is that, “there is no sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010”.

Answer 33

Explanation of Solution

Conclusion:

From the given information, the null hypothesis is not rejected. Thus, there is no enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 34

e.

Expert Solution

To determine

To state: The conclusion based on the results of the test.

Answer to Problem 1RE

The conclusion is that, “there is sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Explanation of Solution

From the given information, the null hypothesis is rejected. Thus, there is enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 35

e.

Expert Solution

Answer 36

e.

Expert Solution

Answer 37

Expert Solution

Answer 38

To determine

To state: The conclusion based on the results of the test.

Answer 39

Answer to Problem 1RE

The conclusion is that, “there is sufficient evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.

Answer 40

Explanation of Solution

From the given information, the null hypothesis is rejected. Thus, there is enough evidence to infer that the mean outstanding credit card debt of college graduates has been decreased since 2010.