Chapter 10.3, Problem 98E

To determine

To find out from the option that which of the following is the correct interpretation of the P -value.

Answer to Problem 98E

Option (d) 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. and the P -value is given that:

  $\begin{array}{l}{H}_0:{\mu }_{A-B}=0\\ H_a:{\mu }_{A-B}\ne 0\\ P=0.227=22.7\%\end{array}$

The P -value is the probability of obtaining the sample results or more extreme assuming the null hypothesis is true.

Also,

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

Thus, the test is two sided and the P -value is then refers to the probability of obtaining a sample mean of the difference of at most $-0.34\text{ or at least 0}\text{.34}$ . Moreover, the probability value only holds when the null hypothesis is true and thus when the true mean is zero.

Thus, the correct option is (d) then.