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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

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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Subscribe now to access step-by-step solutions to millions of textbook problems written by subject matter experts!

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.