s 79 Suppose that we will take a random sample of size n fro

s 7.9 Suppose that we will take a random sample of size n from a population having mean mu and standard deviation sigma. For each of the following situations, find the mean, variance, and standard deviation of the sampling distribution of the sample mean X: a mu = 10, sigma = 2, n = 25 C mu = 3, sigma = .1, n = 4 b mu = 500, sigma = .5, n = 100 d mu = 100, sigma = 1, n = 1,600 7.10 For each situation in Exercise 7.9, find an interval that contains (approximately or exactly) 99.73 percent of all the possible sample means. In which cases must we assume that the population is normally distributed? Why?

Solution

Note that the mean of the sample distirbution is also mu (the population mean).

Also, the variance and standard deviation of Xbar is

s^2 (variance)= sigma^2/n
s (standard deviation) = sigma/sqrt(n)

Thus:

A.

u(X) = 10
sigma^2 (X) = 0.16
sigma (X) = 0.4

B.

u(X) =    500
sigma^2(X) =    0.0025
sigma(X) =    0.05

C.

u(X) =    3
sigma^2(X) =    0.0025
sigma(X) =    0.05

D.

u(X) =    100
sigma^2(X) =    0.000625
sigma(X) =    0.025

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