The following data represent soil water content (percent water by volume) for independent random samples of soil taken from two experimental fields growing bell peppers Soil water content from field I: x1;n1=72
15.1 11.2 10.3 10.8 16.6 8.3 9.1 12.3 9.1 14.3
10.7 16.1 10.2 15.2 8.9 9.5 9.6 11.3 14.0 11.3
15.6 11.2 13.8 9.0 8.4 8.2 12.0 13.9 11.6 16.0
9.6 11.4 8.4 8.0 14.1 10.9 13.2 13.8 14.6 10.2
11.5 13.1 14.7 12.5 10.2 11.8 11.0 12.7 10.3 10.8
11.0 12.6 10.8 9.6 11.5 10.6 11.7 10.1 9.7 9.7
11.2 9.8 10.3 11.9 9.7 11.3 10.4 12.0 11.0 10.7
8.8 11.1
Soil water content from field II: x2;n2=80
12.1 10.2 13.6 8.1 13.5 7.8 11.8 7.7 8.1 9.2
14.1 8.9 13.9 7.5 12.6 7.3 14.9 12.2 7.6 8.9
13.9 8.4 13.4 7.1 12.4 7.6 9.9 26.0 7.3 7.4
14.3 8.4 13.2 7.3 11.3 7.5 9.7 12.3 6.9 7.6
13.8 7.5 13.3 8.0 11.3 6.8 7.4 11.7 11.8 7.7
12.6 7.7 13.2 13.9 10.4 12.8 7.6 10.7 10.7 10.9
12.5 11.3 10.7 13.2 8.9 12.9 7.7 9.7 9.7 11.4
11.9 13.4 9.2 13.4 8.8 11.9 7.1 8.5 14.0 14.2
A. Use a calculator with mean and standard deviation keys to verify that x1=11.42, s1=2.08, x2=10.65, and s2=3.03
B. Let m1 be the population mean for x1 and let m2 be the population mean for x2. Find a 95 percent confidence interval for m1-m2.
C. Interpretation: Explain what the confidence interval means in the context of this problem. Does the interval consist of numbers that are all positive? all negative? of different signs? At the 95 percent level of confidence, is the population mean soil water content of the first field higher than that of the second field?
D. Which distribution (standard normal or Student's t) did you use? Why? Do you need information about the soil water content distributions?