Archaeology: Independent random samples from two regions (not those cited in Problem 11) gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions. Region I: x1; n1=15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010 Region II: x2; n2=14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020 (a) Use a calculator with mean and standard deviation keys to verify that x1 < 1387.3, s1 < 498.3, x2 < 1039.3, and s2 < 346.7. (b) Let m1 be the population mean for x1 and let m2 be the population mean for x2. Find an 80% confidence interval for u1-u2. (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 80% level of confidence, is one region more interesting than the other from a geochemical perspective? (d) Check Requirements Which distribution (standard normal or Student’s t) did you use? Why?
Archaeology: Independent random samples from two regions (not those cited in Problem 11) gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions.
Region I: x1; n1=15 855 1550 1230 875 1080 2330 1850 1860 2340 1080 910 1130 1450 1260 1010
Region II: x2; n2=14 540 810 790 1230 1770 960 1650 860 890 640 1180 1160 1050 1020
(a) Use a calculator with mean and standard deviation keys to verify that x1 < 1387.3, s1 < 498.3, x2 < 1039.3, and s2 < 346.7.
(b) Let m1 be the population mean for x1 and let m2 be the population mean for x2. Find an 80% confidence interval for u1-u2.
(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 80% level of confidence, is one region more interesting than the other from a geochemical perspective?
(d) Check Requirements Which distribution (standard normal or Student’s t) did you use? Why?
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