Maurice Tutor

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Category > Management Posted 13 Oct 2017 My Price 8.00

ancient Peru­ vian hairs

5.11.  .55A physical anthropologist performed a mineral analysis of nine ancient Peru­ vian hairs.  The results for the chromium ( x1 ) and strontium ( x2) levels, in parts per million (ppm), were as follows:

 

x1(Cr)

.48

40.53

2.19

 

.74

.66

.93

.37

.22

x2(Cr)

12.57

73.68

11 .13

20 .03

20.29

.78

4.64

.43

1.08

Source: Benfer and others, "Mineral Analysis of Ancient Peruvian Hair,"

American Journal ofPhysical Anthropo logy, 48, no. 3 (1978), 277-282.

 

 

It is known that low levels (less than or equal to .100 ppm) of chromium sug­ gest the presence of diabetes. while strontium is an indication of animal pro­ tein intake.

(a) Construct and plot a 90% joint confidence ellipse for the population mean vector IL' == [,u1 , ,u2], 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 ,u1 and ,u2 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   (,u1

arbitrary, 10) in the  confidence regions?  Is  [.30, 10] '  a plausible value   for

IL? Discuss.

(c) Do these data appear to be bivariate normal? Discuss their status with ref­

erence 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.

 

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Maurice Tutor
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Status NEW Posted 13 Oct 2017 10:10 PM My Price 8.00

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