Chapter 10: Q. 15 (page 668)

Mrs. Woods and Mrs. Bryan are avid vegetable gardeners. They use different fertilizers, and each claims that hers is the best fertilizer to use when growing tomatoes. Both agree to do a study using the weight of their tomatoes as the response variable. They had each planted the same varieties of tomatoes on the same day and fertilized the plants on the same schedule throughout the growing season. At harvest time, they each randomly select $15$ tomatoes from their respective gardens and weigh them. After performing a two-sample t-test on the difference in mean weights of tomatoes, they get $t = 5.24$ and $P = 0.0008$ . Can the gardener with the larger mean claim that her fertilizer caused her tomatoes to be heavier?
(a) No, because the soil conditions in the two gardens is a potential confounding variable.
(b) No, because there was no replication.
(c) Yes, because a different fertilizer was used on each garden.
(d) Yes, because random samples were taken from each garden.

Short Answer

Expert verified

The gardener with the larger mean can not claim that her fertilizer caused her tomatoes to be heavier (a) No because the soil conditions in the two gardens are a potential confounding variable.

Step by step solution

Given Information

We are given that At harvest time, they each randomly select 15 tomatoes from their respective gardens and weigh them. After performing a two-sample t-test on the difference in mean weights of tomatoes, they get $t = 5.24$ and $P = 0.0008$

Explanation

According to question for comparison , all factors must be same. whether the p-value is less than alpha. maybe, condition of one soil patch will be better than other soil patch.

P-value less than alpha means that there is some association.

Therefore, the gardener with the larger mean can not claim that her fertilizer caused her tomatoes to be heavier . because the soil condition in two gardens is a potential confounding variable.