Chapter 17, Problem 17.21CYS

To determine

The value of $H_0$ by the computed probability.

Answer to Problem 17.21CYS

The correct option is (a) true, of the test statistic taking a value as extreme as or more extreme than that actually observed is 0.008.

Explanation of Solution

Given info:

The P-value is 0.008.

Justification:

Reason for correct answer:

Since the definition of P-value says that the probability that the test statistics take the value, which is extreme or more extreme than the actual observed value under the assumption, that $H_0$ is true, thus as the value of P is 0.008, then the test statistic taking a value as extreme as or more extreme than that actually observed is 0.008.

Thus, option (a) $H_0$ is true, of the test statistic taking a value as extreme as or more extreme than that actually observed is 0.008 is correct.

Reason for incorrect answers:

Option (b) says that $H_0$ is true, of the test statistic taking a value as extreme as or less extreme than that actually observed is 0.008 which is incorrect because by the definition of P-value, $H_0$ is true, of the test statistic taking a value as extreme as or more extreme than that actually observed.

Option (c) says that $H_0$ is false, of the test statistic taking a value as extreme as or more extreme than that actually observed is 0.008 which is incorrect because by the definition of P-value, $H_0$ is true, of the test statistic taking a value as extreme as or more extreme than that actually observed.

Thus, options (b) and (c) are incorrect.

Conclusion:

Thus, $H_0$ is true, of the test statistic taking a value as extreme as or more extreme than that actually observed is 0.008.

Statistics Concept Introduction

Introduction:

P-value:

The probability that the test statistics take the value that is extreme or more extreme than the actual observed value under the assumption that $H_0$ is true.