Chapter 21, Problem 3E

a.

To determine

Check whether the statement is true or false.

Answer to Problem 3E

The given statement is false.

Explanation of Solution

Justification:

If the P-value is high, then the null hypothesis is not rejected. Thus, there is no strong evidence that the null hypothesis is false.

b.

To determine

Check whether the statement is true or false.

Answer to Problem 3E

The statement is false.

Explanation of Solution

Justification:

When the P-value is less, the result provides the evidence against the null hypothesis. It means that the value of the hypothesis test says that the null hypothesis is rejected and does not state that it is false.

c.

To determine

Check whether the statement is true or false.

Answer to Problem 3E

The statement is false.

Explanation of Solution

Justification:

Since the high P-value does not mean that the null hypothesis is true, it proves that the data are consistent with the null hypothesis. However, it does not have any evidence to prove that the null hypothesis is true.

d.

To determine

Check whether the statement is true or false.

Answer to Problem 3E

The statement is false.

Explanation of Solution

Justification:

If the P-value is less than 0.05, then there is enough evidence to prove that the null hypothesis is rejected. The rejection of null hypothesis depends on the risk of type-I error that depends on the researcher’s willingness to assume the level of significance.

Statistics Concept Introduction

Introduction:

P-value:

The P-value represents the probability value that 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 obtains the test statistic is extreme or more extreme from the population parameter if the null hypothesis is true.

Criterion for rejecting the null hypothesis using the 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 $H_0$.