When the population distribution is normal and n is large, the sample standard deviation S has approximately
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a. Assuming that the underlying distribution is normal, what is an approximately unbiased estimator of the 99th percentile θ = μ + 2.33σ?
b. When the Xi's are normal, it can be shown that and S are independent rv's (one measures location whereas the other measures spread). Use this to compute V(θ) and σθ for the estimator θ of part (a). What is the estimated standard error θ?
c. Write a test statistic for testing H0: θ = θ0 that has approximately a standard normal distribution when H0 is true. If soil pH is normally distributed in a certain region and 64 soil samples yield = 6.33, s = .16, does this provide strong evidence for concluding that at most 99% of all possible samples would have a pH of less than 6.75? Test using α = .01.
Distribution
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Related Book For
Probability And Statistics For Engineering And The Sciences
ISBN: 9781305251809
9th Edition
Authors: Jay L. Devore
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