Chapter 19, Problem 1E

a.

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 about the test. Moreover, the level of significance is not mentioned. If the level of significance is greater than 0.01 one can conclude that the hypothesis is false, otherwise it is possible to conclude that hypothesis is false. Hence, without the level of significance the claim is not meaningful. Hence, the sentence is false.

b.

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 can be defined as the probability of obtaining a test statistics value as extreme as or more extreme than the observed value, if the null hypothesis is actually true.

The P-value does not mean that the null hypothesis has a 0.01 chance of being true.

c.

To determine

Check whether the statement is true or false.

Answer to Problem 1E

The statement is true.

Explanation of Solution

Justification:

The P-value can be defined as the probability of obtaining a test statistics value as extreme as or more extreme than the observed value, if the null hypothesis is actually true.

As in a test it is needed to nullify the null hypothesis, hence, a P-value of any value provide the evidence against the null hypothesis.

Thus, the statement is true.

d.

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 about the test. Moreover, the level of significance is not mentioned. If the level of significance is equal to 0.01 one can reject the null hypothesis. Otherwise, it is not possible to reject the null hypothesis.

Hence, the statement is false.

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 $H_0$.