A calculator with a random number generator produces the following sequence of r

Question

A calculator with a random number generator produces the following sequence of random numbers: 0.276, 0.123, 0.072, 0.324, 0.815, 0.312, 0.283, 0.717.

a) Find the sample mean.

b)If the calculator produces three digit random numbers that are uniformly distributed between 0.000 and 0.999, find the variance of the sample mean.

c) How large should the sample size be in order to obtain a sample mean whose standard deviation is no greater than 0.01?

d) For the random numbers given, find the sample variance if an unbiased estimator is used.

e) Find the Variance of the estimate of the population variance.

Explanation / Answer

a) sample mean = (0.276+0.123+ 0.072+0.324+ 0.815+ 0.312+0.283+0.717)/8 = 0.3653

b) a= 0.000, b= 0.999

for uniform distribution, variance = (b-a)^2/12 = 0.0832

c) variance in the previous step = 0.0832

so standard deviation is 0.2884

0.2884 / sqrt(n) <= 0.01

sqrt(n) <= 28.84

n=832

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