Chapter 9.3, Problem 103E

To determine

To find: The P -value.

Answer to Problem 103E

The P -value lies between 0.01 and 0.02

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample size}\left(n\right)=20\\ \text{Test statistic}\left(t\right)=-2.25\end{array}$

The null and alternative hypotheses are:

  $\begin{array}{l}{H}_0:\mu =10\\ H_a:\mu <10\end{array}$

Calculation:

The alternative hypothesis suggests that the test is one tailed.

The degree of freedom can be calculated as:

  $\begin{array}{c}\text{Degree of freedom}\left(df\right)=n-1\\ =20-1\\ =19\end{array}$

The p -value can be calculated as:

  $\begin{array}{c}P-value=P\left(t>\left|t\right|\right)\\ =P\left(t>|-2.25|\right)\\ =0.018\end{array}$

Thus, it could be said that P -value lies between 0.01 and 0.02.

Hence, the correct option is (a).