An agriculturalist on a farm conducted a study to investigate whether ladybugs are effective in reducing damage

cause by moths to the fruit of avocado trees. The agriculturalist randomly sampled 66 avocado 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 green house 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 the 33 pairs and is shown in the stem plot below.

Difference in Number of Damaged Avocado Fruit

Per Avocado Tree Pair

-3 0 5 8 9

-2 3 7 7 8

-1 1 3 4

-0 9

0 0 0 5 8 9

1 0 2 7 9

2 6 6

3 2 2 4 4

4 2 3 4 5

5 0 2

Key: = 52 Damaged Avocado Fruit

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

b) Based only on the sample data in the stem plot, 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.

5 2

The owner of the farm will introduce ladybugs to all of his avocado trees if the agriculturalist can provide

convincing statistical evidence that the ladybugs are effective in reducing the number of damaged avocado

fruit over a one-month period.

c) State, in words, the hypotheses of the appropriate test the agriculturalist should use to investigate whether

the sample data provides convincing statistical evidence that the ladybugs are effective in reducing the

number of damaged avocado fruit over a one-month period.

d) Assuming all conditions for the appropriate test are met, the agriculturalist reported a p-value of 0.072 for

the test. Based on the p-value and

= 0.05

, would the owner of the farm introduce the ladybugs? Explain

your answer.

Consider a scenario in which 5 tree pairs are randomly selected one at a time, with replacement, from the

sample of 33 tree pairs. Let the random variable T represent the number of tree pairs out of the 5 selected

with a positive difference in number of damaged avocado fruit.

e) Calculate and interpret the value of

T

in the context of the scenario.

f) Describe how the scenario could be modified to make T a geometric random variable.