A physical anthropologist performed a mineral analysis of nine ancient Peruvian hairs. The results for the chromium (x₁) and strontium (x₂) levels, in parts per million (ppm), were as follows:

It is known that low levels (less than or equal to .100 ppm) of chromium suggest the presence of diabetes, while strontium is an indication of animal protein intake.

(a) Construct and plot a 90% joint confidence ellipse for the population mean vector - [1.4, ln], assuming that these nine Peruvian hairs represent a random sample from individuals belonging to a particular ancient Peruvian culture.

(b) Obtain the individual simultaneous 90% confidence intervals for μ₁ and μ₂ by" projecting" the ellipse constructed in Part a on each coordinate axis. (Alternatively, we could use Result 5.3.) Does it appear as if this Peruvian culture has a mean strontium level of 10? That is, are any of the points (μ₁arbitrary,10) in the confidence regions? Is (.30,10r a plausible value for μ? Discuss.

(c) Do these data appear to be bivariate normal? Discuss their status with reference to Q-Q plots and a scatter diagram. If the data are not bivariate normal, what implications does this have for the results in Parts a and b?

(d) Repeat the analysis with the obvious "outlying" observation removed. Do the inferences change? Comment.