Question

Cloud seeding. It has long been a dream of farmers to summon rain when it is needed for their crops. Crop losses to drought have significant economic impact. One possibility is cloud seeding, in which chemicals

are dropped into clouds in an attempt to induce rain. Simpson, Alsen, and Eden (Technometrics, 1975) report the results of trials in which clouds were seeded and the amount of rainfall recorded. The authors report on 26 seeded (Group 2) and 26 unseeded (Group 1) clouds. Each group has been sorted in order of the amount of rainfall, largest amount first. Here are two possible tests to study the question of whether
cloud seeding works.

Paired t-Test of m11-22

Mean of Paired Differences=-277.4

t-Statistic=-3.641 w>25 dfp=0.0012

2-Sample t-test of m1-m2

Difference Between Means=-277.4

t-Statistic=-1.998w>33 dfp=0.0538

Which of these tests is appropriate for these data? Explain.

Answer 1

The appropriate test for the given data on cloud seeding is the paired t-test, as it is designed for related samples and has shown a statistically significant result in this case.

Step-by-step explanation:

The question pertains to deciding whether a paired t-test or a two-sample t-test is more suitable for data from trials on cloud seeding. When comparing two related groups, such as the same cloud being tested once with seeding and once without, a paired t-test is appropriate because it accounts for the natural variance between the paired observations. The paired t-test here reports a t-Statistic of -3.641 with a p-value of 0.0012, indicating a statistically significant difference between the two conditions. On the other hand, a two-sample t-test is used when comparing two independent groups, which in this case, the clouds are treated as unrelated. This yields a t-statistic of -1.998 with a p-value of 0.0538, sitting on the edge of the conventional significance level of 0.05.

The paired t-test should be chosen for this analysis because it is designed for the comparison of two related samples (seeded vs. unseeded clouds) and typically has more power to detect differences than the two-sample t-test when the paired observations are indeed related.