Agriculture: Bell Peppers The following data represent

Chapter , Problem 13

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Agriculture: Bell Peppers 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 (Reference: Journal of Agricultural, Biological, and Environmental Statistics). Note: These data are also available for download on-line in HM StatSPACE 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 s1 2.08, 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% 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% 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 Students t) did you use? Why? Do you need information about the soil water content distributions?