Chapter 10.3, Problem 97E

To determine

To find from the following option a $95\%$ confidence interval for ${\mu }_{A-B}$ is given by which option.

Answer to Problem 97E

Option (e) is the correct option.

Explanation of Solution

It is given that there are two varieties of tomato i.e. Variety A and Variety B. Then the researcher wants to claim that the variety A have a different average yield from that of variety B. we have to find out the confidence interval from the option.

Thus,

  $\begin{array}{l}n=10\\ {\overline{x}}_{A-B}=0.34\\ s_{A-B}=0.83\\ c=0.95\end{array}$

Thus the degree of freedom will be:

  $\begin{array}{l}df=n-1\\ =10-1\\ =9\end{array}$

And the t -value will be:

  $t_{\alpha /2}=2.262$

Thus the confidence interval will be:

  $\begin{array}{l}\overline{x}\pm t_{\alpha /2}\times \frac{s}{\sqrt{n}}\\ =0.34\pm 2.262\times \frac{0.83}{\sqrt{10}}\end{array}$

Thus, option (e) is the correct option.