Chapter 13, Problem 35SE

Rainfall In a well-known study on the effects of cloud seeding to produce rainfall (cited on page 659 of the text by Simpson et. al), experimenters randomly assigned airplanes to release either silver nitrate (which is believed to increase the amount of rainfall from a cloud) or a placebo. Fifty-two clouds were chosen at random; half were “seeded” with silver nitrate, and half were not. In the text, we compared the median rainfall amounts for the seeded (silver nitrate) and unseeded clouds. In this exercise, you will compare the mean rainfall amounts for the seeded and unseeded clouds.

In the study, the seeded clouds produced more rain, on average, by 368.9 acre-feet. 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 mean of each stack and found the difference. This was actually done by a computer and repeated 1000 times. The results are shown in the histogram.

Carry out a hypothesis test to determine whether cloud seeding increased the mean rainfall. By referring to the histogram, choose from the following possible p-values (one-tailed):

0.50, 0.25, 0.15, 0.025, less than 0.0001

Use a 5% significance level for your test.