Question

Researchers suspect that Variety A tomato plants have a different average yield than Variety B tomato plants. To find out, researchers randomly select$10$Variety A and$10$Variety B tomato plants. Then the researchers divide in half each of$10$small plots of land in different locations. For each plot, a coin toss determines which half of the plot gets a Variety A plant; a Variety B plant goes in the other half. After harvest, they compare the yield in pounds for the plants at each location. The$10$differences (Variety A − Variety B) in yield are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. The mean difference is $\stackrel{-}{x}=0.34$$\frac{305}{1526}=0.200=20\%{\stackrel{-}{x}}_{A-B}=0.34$and the standard deviation of the differences is s A-B$=0.83$$\frac{305}{1526}=0.200=20\%=s_{A-B}=0.83$.Let${\mu }_{A-B}=\frac{305}{1526}=0.200=20\%$μA−B = the true mean difference (Variety A − Variety B) in yield for tomato plants of these two varieties.

The P-value for a test of H0: μA−B=0$\frac{305}{1526}=0.200=20\%$versus Ha: μA−B≠0 is 0.227. Which of the following is the

correct interpretation of this P-value?

a. The probability that μA−B is$0.227$.

b. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is$0$, the probability of getting a sample mean difference of$0.34$is$0.227$.

c. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is$0$, the probability of getting a sample mean difference of$0.34$or greater is$0.227$.

d. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is$0$, the probability of getting a sample mean difference greater than or equal to$0.34$or less than or equal to −$0.34$is$0.227$.

e. Given that the true mean difference (Variety A – Variety B) in yield for these two varieties of tomato plants is not 0, the probability of getting a sample mean difference greater than or equal to $0.34$or less than or equal to −$0.34$is$0.227$.

Short answer

The correct option is (d) The true mean difference is$0$and the probability of getting a sample mean difference is greater than or equal to$0.34$or less than or equal to$-0.34$is$0.227$.

Step-by-step solution

Given Information

We are given theP-value and we have to find out which value will be satisfied from the given options.

Explanation

According to the question,

the $H_0:{\mu }_{A-B}=0,H_{\alpha }:{\mu }_{A-B}\ne 0,\stackrel{-}{x}=0.34andP-value=0.227$

The P-value is known as the probability of obtaining the sample results or extreme. The true difference is$0.34$that, as there is no boundary, it is two-sided and that is why the P-value is greater than or equal to$0.34$or less than or equal to$0.34$and as the null hypothesis, the H value is considered to be zero, which implies that the true difference is also$0$.

Hence, option (d) is correct.