5.20.     A wildlife ecologist measured x1  = tail length (in millimeters) and x2  = wing length (in millimeters) for a sample of n = 45 female hook-billed kites.  These data are displayed in Table 5.12.  Using the data in the table,

 

TABLE 5. 12   BIRD DATA

 

 

(a)  Find and sketch the 95% confidence  ellipse  for  the  population means  f.LI and JL2 . Suppose it is known that JL1 = 190 mm and JL2 = 275 mm for male hook-billed kites. Are these plausible values for the  mean tail length  and mean wing length for the female birds? Explain.

(b) Construct the simultaneous 95% T2-intervals for JLI and JL2 and the 95%

Bonferroni intervals for JL1 and JL2 •     Compare the two sets of intervals.   What

advantage, if any, do the T2-intervals have over the Bonferroni  intervals?

(c) Is the bivariate normal distribution a viable population model? Explain

with reference to Q-Q plots and a scatter diagram.

 

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