Chapter 13, Problem 36SE

Rainfall Refer to exercise 13.35, which discussed a study on the effects of cloud seeding to produce rainfall. Some researchers think that cloud seeding has little effect on “low rain potential” clouds. Instead, they claim, most of the action is with clouds that would produce lots of rain even without seeding. In this scenario, clouds that would produce little rain without seeding will produce little rain with seeding. However, the clouds that would produce the most rain without seeding will produce much, much more rain with cloud seeding. To test this, researchers carried out a randomization test to find out whether the third quartile of rainfall increased under cloud seeding. The table gives summary statistics.

a. Explain what it means to say that the third quartile of rainfall is 474.30 acre-feet.

b. Why is the third quartile an appropriate statistic to answer the research-ers’ question?

c. What is the observed difference in third-quartile rainfall between the seeded and unseeded clouds?

d. To determine whether such differences could occur by chance, a statistician could have written the 52 rainfall amounts on separate slips of paper and randomly dealt them into two stacks. He or she would then have computed the third quartile of each stack and found the difference. A computer actually did this 1000 times, each time finding the difference between the third quartile for the seeded clouds minus the third quartile for the unseeded clouds. The results are shown in the histogram. Referring to the histogram, carry out a hypothesis test to test whether cloud seeding increased the third-quartile rainfall. (You will have to get approximate $p$ -values by reading the histogram.) (Remember that you need only decide whether the $p$ -value is larger or smaller than 0.05.)