This and the next two problems are based on discussions and data in Le Cam and Neyman (1...

This and the next two problems are based on discussions and data in Le Cam and Neyman (1967), which is devoted to the analysis of weather modification experiments. The examples illustrate some ways in which principles of experimental design have been used in this field. During the summers of 1957 through 1960, a series of randomized cloud-seeding experiments were carried out in the mountains of Arizona. Of each pair of successive days, one day was randomly selected for seeding to be done. The seeding was done during a two-hour to four-hour period starting at midday, and rainfall during the afternoon was measured by a network of 29 gauges. The data for the four years are given in the following table (in inches). Observations in this table are listed in chronological order.

a. Analyze the data for each year and for the years pooled together to see if there appears to be any effect due to seeding. You should use graphical descriptive methods to get a qualitative impression of the results and hypothesis tests to assess the significance of the results.

b. Why should the day on which seeding is to be done be chosen at random rather than just alternating seeded and unseeded days? Why should the days be paired at all, rather than just deciding randomly which days to seed?