2. Exercise 2 Samples are taken from a population of heifers with known mean and

Question

2. Exercise 2 Samples are taken from a population of heifers with known mean and variance of weight gains equal to 80 kg and 324 kg12, respectively mean = variance = 80 324 7 a. What are the mean and variance of the average weight gain of random samples of 20 heifers? [8] 20 r= mean of averages = 0 variance of averages 2 b. What are the mean and variance of the average weight gain of random samples of 30 heifers? [5] 30 rE mean of averages = 5 6 variance of averages 8 c. How many heifers have to be sampled for the variance of the average weight to equal 12.96? [5] 9 0 1 S2 variance of average- 2.96

Explanation / Answer

Sol:

population mean=80

population variance=324

SOlutiona:

sample mean=population mean=80

sample variance=population variance/sqrt(sample size)

=324/sqrt(20)

=72.45

Solutionb:

mean of avergaes=80

variance of averages=324/sqrt(80)

=36.22

Solutionc:

sigma^2/sqrt(r)=12.96

324/sqrt(r)=12.96

324/12.96=sqrt(n)

sqrt(r)=25

squaring on bothisdes

r=25*25

r=625

sample size=625

r=625

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