True or false Which of the following are true? If false, explain briefly. a) A P-value of 0.01 means that the null hypothesis is false. b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true. c) A P-value of 0.01 is evidence against the null hypothesis. d) A P-value of 0.01 means we should definitely reject the null hypothesis.

Question

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Answer 1

Textbook Question

Chapter 16, Problem 1E

True or false Which of the following are true? If false, explain briefly.

a) A P-value of 0.01 means that the null hypothesis is false.
b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.
c) A P-value of 0.01 is evidence against the null hypothesis.
d) A P-value of 0.01 means we should definitely reject the null hypothesis.

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

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The statement provides the evidence against the null hypothesis. It does not mean that the null hypothesis is false. It means null hypothesis is not true.

b.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The P-value does not mean the probability value of null hypothesis; it means the value of the hypothesis test.

c.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is true.

Explanation of Solution

Justification:

Since, the P-value is less than the any other level of significance, the null hypothesis is rejected. Thus, the P-value of 0.01 is evidence against the null hypothesis.

d.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

Since the P-value of 0.01 have the enough evidence to reject the null hypothesis and purely depends on the risk of type-I error assumed by the researcher.

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value which is associated with a statistical test. The difference between an observed mean (sample mean difference between scores) and a population mean (mean difference between scores) is likely to be supported when the null hypothesis is true. That is, the P-value is defined as the probability that obtaining the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting null hypothesis using P-value approach:

Decision rule:

If P-value≤α, then reject the null hypothesis H0.

If P-value>α, then fail to reject the null hypothesis H0.

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Answer 2

Textbook Question

Chapter 16, Problem 1E

True or false Which of the following are true? If false, explain briefly.

a) A P-value of 0.01 means that the null hypothesis is false.
b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.
c) A P-value of 0.01 is evidence against the null hypothesis.
d) A P-value of 0.01 means we should definitely reject the null hypothesis.

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

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The statement provides the evidence against the null hypothesis. It does not mean that the null hypothesis is false. It means null hypothesis is not true.

b.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The P-value does not mean the probability value of null hypothesis; it means the value of the hypothesis test.

c.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is true.

Explanation of Solution

Justification:

Since, the P-value is less than the any other level of significance, the null hypothesis is rejected. Thus, the P-value of 0.01 is evidence against the null hypothesis.

d.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

Since the P-value of 0.01 have the enough evidence to reject the null hypothesis and purely depends on the risk of type-I error assumed by the researcher.

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value which is associated with a statistical test. The difference between an observed mean (sample mean difference between scores) and a population mean (mean difference between scores) is likely to be supported when the null hypothesis is true. That is, the P-value is defined as the probability that obtaining the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting null hypothesis using P-value approach:

Decision rule:

If P-value≤α, then reject the null hypothesis H0.

If P-value>α, then fail to reject the null hypothesis H0.

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Answer 3

Textbook Question

Chapter 16, Problem 1E

True or false Which of the following are true? If false, explain briefly.

a) A P-value of 0.01 means that the null hypothesis is false.
b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.
c) A P-value of 0.01 is evidence against the null hypothesis.
d) A P-value of 0.01 means we should definitely reject the null hypothesis.

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

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The statement provides the evidence against the null hypothesis. It does not mean that the null hypothesis is false. It means null hypothesis is not true.

b.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The P-value does not mean the probability value of null hypothesis; it means the value of the hypothesis test.

c.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is true.

Explanation of Solution

Justification:

Since, the P-value is less than the any other level of significance, the null hypothesis is rejected. Thus, the P-value of 0.01 is evidence against the null hypothesis.

d.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

Since the P-value of 0.01 have the enough evidence to reject the null hypothesis and purely depends on the risk of type-I error assumed by the researcher.

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value which is associated with a statistical test. The difference between an observed mean (sample mean difference between scores) and a population mean (mean difference between scores) is likely to be supported when the null hypothesis is true. That is, the P-value is defined as the probability that obtaining the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting null hypothesis using P-value approach:

Decision rule:

If P-value≤α, then reject the null hypothesis H0.

If P-value>α, then fail to reject the null hypothesis H0.

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

Answer 4

Textbook Question

Chapter 16, Problem 1E

True or false Which of the following are true? If false, explain briefly.

a) A P-value of 0.01 means that the null hypothesis is false.
b) A P-value of 0.01 means that the null hypothesis has a 0.01 chance of being true.
c) A P-value of 0.01 is evidence against the null hypothesis.
d) A P-value of 0.01 means we should definitely reject the null hypothesis.

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

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The statement provides the evidence against the null hypothesis. It does not mean that the null hypothesis is false. It means null hypothesis is not true.

b.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The P-value does not mean the probability value of null hypothesis; it means the value of the hypothesis test.

c.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is true.

Explanation of Solution

Justification:

Since, the P-value is less than the any other level of significance, the null hypothesis is rejected. Thus, the P-value of 0.01 is evidence against the null hypothesis.

d.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

Since the P-value of 0.01 have the enough evidence to reject the null hypothesis and purely depends on the risk of type-I error assumed by the researcher.

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value which is associated with a statistical test. The difference between an observed mean (sample mean difference between scores) and a population mean (mean difference between scores) is likely to be supported when the null hypothesis is true. That is, the P-value is defined as the probability that obtaining the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting null hypothesis using P-value approach:

Decision rule:

If P-value≤α, then reject the null hypothesis H0.

If P-value>α, then fail to reject the null hypothesis H0.

Want to see more full solutions like this?

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

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The statement provides the evidence against the null hypothesis. It does not mean that the null hypothesis is false. It means null hypothesis is not true.

b.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The P-value does not mean the probability value of null hypothesis; it means the value of the hypothesis test.

c.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is true.

Explanation of Solution

Justification:

Since, the P-value is less than the any other level of significance, the null hypothesis is rejected. Thus, the P-value of 0.01 is evidence against the null hypothesis.

d.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

Since the P-value of 0.01 have the enough evidence to reject the null hypothesis and purely depends on the risk of type-I error assumed by the researcher.

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value which is associated with a statistical test. The difference between an observed mean (sample mean difference between scores) and a population mean (mean difference between scores) is likely to be supported when the null hypothesis is true. That is, the P-value is defined as the probability that obtaining the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting null hypothesis using P-value approach:

Decision rule:

If P-value≤α, then reject the null hypothesis H0.

If P-value>α, then fail to reject the null hypothesis H0.

Answer 8

a.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The statement provides the evidence against the null hypothesis. It does not mean that the null hypothesis is false. It means null hypothesis is not true.

Answer 9

a.

Expert Solution

Answer 10

a.

Expert Solution

Answer 11

Expert Solution

Answer 12

To determine

Check whether the statement is true or false.

Answer 13

Answer to Problem 1E

The statement is false.

Answer 14

Explanation of Solution

Justification:

The statement provides the evidence against the null hypothesis. It does not mean that the null hypothesis is false. It means null hypothesis is not true.

Answer 15

b.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

The P-value does not mean the probability value of null hypothesis; it means the value of the hypothesis test.

Answer 16

b.

Expert Solution

Answer 17

b.

Expert Solution

Answer 18

Expert Solution

Answer 19

To determine

Check whether the statement is true or false.

Answer 20

Answer to Problem 1E

The statement is false.

Answer 21

Explanation of Solution

Justification:

The P-value does not mean the probability value of null hypothesis; it means the value of the hypothesis test.

Answer 22

c.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is true.

Explanation of Solution

Justification:

Since, the P-value is less than the any other level of significance, the null hypothesis is rejected. Thus, the P-value of 0.01 is evidence against the null hypothesis.

Answer 23

c.

Expert Solution

Answer 24

c.

Expert Solution

Answer 25

Expert Solution

Answer 26

To determine

Check whether the statement is true or false.

Answer 27

Answer to Problem 1E

The statement is true.

Answer 28

Explanation of Solution

Justification:

Since, the P-value is less than the any other level of significance, the null hypothesis is rejected. Thus, the P-value of 0.01 is evidence against the null hypothesis.

Answer 29

d.

Expert Solution

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is false.

Explanation of Solution

Justification:

Since the P-value of 0.01 have the enough evidence to reject the null hypothesis and purely depends on the risk of type-I error assumed by the researcher.

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value which is associated with a statistical test. The difference between an observed mean (sample mean difference between scores) and a population mean (mean difference between scores) is likely to be supported when the null hypothesis is true. That is, the P-value is defined as the probability that obtaining the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting null hypothesis using P-value approach:

Decision rule:

If P-value≤α, then reject the null hypothesis H0.

If P-value>α, then fail to reject the null hypothesis H0.

Answer 30

d.

Expert Solution

Answer 31

d.

Expert Solution

Answer 32

Expert Solution

Answer 33

To determine

Check whether the statement is true or false.

Answer 34

Answer to Problem 1E

The statement is false.

Answer 35

Explanation of Solution

Justification:

Since the P-value of 0.01 have the enough evidence to reject the null hypothesis and purely depends on the risk of type-I error assumed by the researcher.

Answer 36

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value which is associated with a statistical test. The difference between an observed mean (sample mean difference between scores) and a population mean (mean difference between scores) is likely to be supported when the null hypothesis is true. That is, the P-value is defined as the probability that obtaining the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting null hypothesis using P-value approach:

Decision rule:

If P-value≤α, then reject the null hypothesis H0.

If P-value>α, then fail to reject the null hypothesis H0.