An agriculturalist on a farm conducted a study to investigate whether ladybugs are effective in reducing damage caused by moths to the fruit of avocado trees. The agriculturalist randomly sampled66avocado trees from the farm and paired them based on size. One tree from each pair was randomly assigned to a greenhouse with ladybugs, and the other tree in the pair was assigned to a greenhouse without ladybugs. After one month, the number of damaged avocado fruit on each tree was recorded. All other variables were held constant over the one month period. The difference in the number of damaged avocado fruit per tree pair (without ladybugs minus with ladybugs) was calculated for each of the33pairs and is shown in the stemplot.

Explain what a positive difference indicates in the context of the study.

(b) Based only on the sample data in the stemplot, should the ladybugs be used to help reduce damage to the fruit? Explain your reasoning in the context of the study. Do not perform an inferential procedure.

Consider a scenario in which5tree pairs are randomly selected one at a time, with replacement, from the sample of33tree pairs. Let the random variableTrepresent the number of tree pairs out of the5selected with a positive difference in number of damaged avocado fruit.

(c)Calculate and interpret the value ofTin the context of the scenario.

(d) Describe how the scenario could be modified to makeTageometricrandom variable.