Chapter 10.2, Problem 69E

To determine

To select which of the following is the correct expression for the $95\%$ confidence interval for the difference in mean word length for these two novels.

Answer to Problem 69E

Option (d) is the correct option.

Explanation of Solution

It is given that:

  $\begin{array}{l}{\overline{x}}_1=4.08\\ {\overline{x}}_2=3.85\\ n_1=30\\ n_2=30\\ s_1=2.40\\ s_2=2.26\\ \alpha =0.05\end{array}$

Now, the degree of freedom will be:

  $\begin{array}{l}df=\min (n_1-1,n_2-1)\\ =\min (30-1,30-1)\\ =29\end{array}$

And the t -value will be as:

  $t_{\alpha /2}=2.045$

Thus, the confidence interval will be as:

  $\begin{array}{l}({\overline{x}}_1-{\overline{x}}_2)\pm t_{\alpha /2}\times \sqrt{\frac{s_1^2}{n_1}+\frac{s_2^2}{n_2}}\\ =(4.08-3.85)\pm 2.045\times \sqrt{\frac{{2.40}^2}{30}+\frac{{2.26}^2}{30}}\end{array}$

This implies that option (d) is the correct option.