Question: Archeology Ireland Please see the setting and reference in Problem 7. Independent random samples from two regions (not those cited in Problem 7 gave the following phosphorous measurements (in ppm). Assume the distribution of phosphorous is mound-shaped and symmetric for these two regions.

Region I: \(x_{1} ; n_{1}=15\)

855 1550 1230 875 1080 2330 1850 1860

2340 1080 910 1130 1450 1260 1010

Region II: \({{x}_{2}};{{n}_{2}}=14\)

540 810 790 1230 1770 960 1650 860

890 640 1180 1160 1050 1020

1. Use a calculator with mean and standard deviation keys to verify that \(\bar{x}_{1}=\) \(1387.3, s_{1} \approx 498.3, \bar{x}_{2} \approx 1039.3\), and \(s_{2} \approx 346.7\)
2. Let \(\mu_{1}\) be the population mean for \(x_{1}\) and let \(\mu_{2}\) be the population mean of \(x_{2} .\) Find an \(80 \%\) confidence interval for \(\mu_{1}-\mu_{2}\)
3. Interpretation: Explain what the confidence interval means in the context 65 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?
4. Which distribution (standard normal or Student's \(t\) ) did you use? Why?

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