Question

Suppose a random sample of n = 25 measurements is selected from a population with mean u and standard deviation o. For each of the following values of u and o, give the values of us and o- a. u = 10,0 = 3 b.u = 100,0 = 25 = c. u = 20, 0 = 40 = d. p = 10,0 = 100 = u

Answer 1

a. u = 10, o = 3

The sample mean (us) is equal to the population mean (u) = 10.

The sample standard deviation (os) is equal to the population standard deviation (o) divided by the square root of the sample size (n) = 3 / sqrt(25) = 1.732.

b. u = 100, o = 25

The sample mean (us) is equal to the population mean (u) = 100.

The sample standard deviation (os) is equal to the population standard deviation (o) divided by the square root of the sample size (n) = 25 / sqrt(25) = 5.

c. u = 20, o = 40

The sample mean (us) is equal to the population mean (u) = 20.

The sample standard deviation (os) is equal to the population standard deviation (o) divided by the square root of the sample size (n) = 40 / sqrt(25) = 16.

d. p = 10, o = 100

This is not a valid case, since the standard deviation cannot be greater than the mean.