Chapter 9.3, Problem 104E

To determine

To find: The test statistics values that are statistically significant.

Answer to Problem 104E

The values are $t<-3.286\text{ or }t>3.326$

Explanation of Solution

Given:

  $\begin{array}{l}\text{Sample size}\left(n\right)=15\\ \text{Level of significance}\left(\alpha \right)=0.05\end{array}$

The null and alternative hypotheses are:

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

Calculation:

The degree of freedom is:

  $\begin{array}{c}\text{Degree of freedom}\left(df\right)=n-1\\ =15-1\\ =14\end{array}$

From critical value table, the critical value at 5% significance level and 14 degree of freedom can be computed as:

  $\begin{array}{c}{t}_{\alpha /2,df}=t_{0.05/2,14}\\ =\pm 3.326\end{array}$

The test would be significant for the values $t<-3.286\text{ or }t>3.326$ .

Hence, the correct option is (d).