Growing tomatoes Researchers suspect that Variety A tomato plants have a higher 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 in yield

(Variety A − Variety B) are recorded. A graph of the differences looks roughly symmetric and single-peaked with no outliers. A paired t test on the differences yields t = 1.295 and P-value = 0.1138.

(a) State appropriate hypotheses for the paired t test. Be sure to define your parameter.

(b) What are the degrees of freedom for the paired t test?

(c) Interpret the P-value in context. What conclusion should the researchers draw?

(d) Describe a Type I error and a Type II error in this setting. Which mistake could researchers have made based on your answer to part (c)?