Chapter 16, Problem 1E

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

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

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.

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.

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.

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 $P\text{-value}\le \alpha$, then reject the null hypothesis $H_0$.

If $P\text{-value}>\alpha$, then fail to reject the null hypothesis $H_0$.