Chapter PVI, Problem 31RE

To determine

To create a $95\%$ confidence interval for the average amount of additional rain created by seeding clouds and explain what your interval means.

Answer to Problem 31RE

We are $95\%$ confident that seeded clouds will produce an average of between $-4.76\text{ and 559}\text{.56}$ more acre feet of rain than unseeded clouds since the interval contains negative values so it may be that seeding is unproductive.

Explanation of Solution

It is given in the question that in an experiment to determine whether seeding clouds with silver iodide increases rainfall and the clouds were randomly assigned to be seeded or not. Thus, to find the confidence interval for mean we will use the calculator $\text{TI}-89$ . In the STAT Intsmenu, choose $4:2-$ SampTInt. You must specify if you are using data stored in two lists or if you will enter the means, standard deviations, and sizes of both samples. You must also indicate whether to pool the variances (when in doubt, say no) and specify the desired level of confidence. So, we have,

	Unseeded	Seeded
Count	26	26
Mean	164.588	441.985
Median	44.2	221.6
SD	278.426	650.787
IntQRange	138.6	337.6
25%tile	24.4	92.4
75%tile	163	430

And $\alpha =0.05$ so by using the calculator $\text{TI}-89$ , the confidence interval will be as:

  $(-4.76,559.56)$ .

Thus, we are $95\%$ confident that seeded clouds will produce an average of between $-4.76\text{ and 559}\text{.56}$ more acre feet of rain than unseeded clouds since the interval contains negative values so it may be that seeding is unproductive.