Chapter 8, Problem 1CQ

To determine

Find the probability of observing a test statistic as extreme as or more extreme than the value actually observed.

Answer to Problem 1CQ

If $\mu =65$, then the probability of observing a test statistic as extreme as or more extreme than the one actually observed is 0.035.

Explanation of Solution

Denote $\mu$ as the true population mean.

The given test hypotheses are:

Null hypothesis: $H_0:\mu =65$.

Alternate hypothesis: $H_1:\mu \ne 65$.

It is given that the P-value is 0.035.

By using the concept of P-value, it is observed that the P-value is the probability of observing a test statistic as extreme as or more extreme than the value actually observed.

Thus, if $\mu =65$, then the probability of observing a test statistic as extreme as or more extreme than the one actually observed is 0.035.

Statistics Concept Introduction

P-value:

P-value is defined as the probability of obtaining a result at least as extreme as the observed value, given that the null hypothesis, $H_0$ is true. The test is said to be statistically significant, when $P\text{-value}<\alpha$, for level of significance $\alpha$.