The weights of male African elements have a normal distribution with a known var
ID: 3251198 • Letter: T
Question
The weights of male African elements have a normal distribution with a known variance of sigma^2= 4,000,000 pounds^2, an unknown mean weight of mu pounds. The mean elephant weight of a random sample of n = 21 male African elephants was 10300 pounds with a sample standard deviation of 500 pounds. We want to create a confidence interval for mu. (measured in pounds) a) What is the critical value for a 99% confidence interval for mu? b) create a 99% confidence interval for mu (, ). c) What is the critical value for an 88% confidence interval for mu? d) Create an 88% confidence interval for mu (, ) e) How many observations would we need to guarantee that the 99% confidence interval has has a length of 500 or less? f) Create a 99% prediction interval for the weight of a single randomly selected male African elephant. (, ). h) Copy your R script for the above into the text box here.Explanation / Answer
e) 2*z* sigma/sqrt(n) = 500
2* 2.575* 1500/500 = sqrt(n)
or n =238.70
Hence, 239 elements should be selected.
f) Confidence interval is (10300 - 1500*2.575 , 10300+1500*2.575) = (6437.5,14162.5)
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