7.5.13. Let Y1.f2, ..., f,, be a random sample of size n from the pdf
Jy (y) = () e-Yl13, y > O; e > O
(a) Use moment-generating functions to show that the ratio 2nf /8 has a chi square distribution with 2n df.
(b) Use the result in Part (a) to derive a 100(1 - a)% confidence interval for e.
7.5.14. Another method for dating rocks was used before the advent of the potassium-a rgon method described i n Case Study 7.5.1. Based on a mineral's lead content, it was cap.able of yielding estimates for this same time period with a standard deviation of 30.4 million years. The potassium-argon method in Case Study 7.5.1 had a smaller sample standard
deviation of J733.4 = 27.1 million years. Is this ''proof ' that the potassium-argon
met.bod is more precise? Using the data in Table 7.5.1, test at the 0.05 level whetaer tae potassium-argon method has a smaller standard deviation t h.an tae older procedwe
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