Question

You have samples of various sizes which you use to estimate a population mean. In the population, the true mean is 100 and the true standard deviation is 10. With which of the following sample sizes are you most likely to see an estimated mean of 135?

a) Sample size 2

b) Sample size 1

c) Sample size 10

d) Sample size 100

Answer 1

Given,

In the population,

the true mean = 100

the true standard deviation = 10.

With estimated mean of 135,

sample size can be 101,

almost nearer to,

d. Sample size 100

n = N*X / (N + X – 1),

where,

X = Zα/2² ­* σ² / MOE²,

and Zα/2 is the critical value of the Normal distribution at α/2 (e.g. for a confidence level of 95%, α is 0.05 and the critical value is 1.96), MOE is the margin of error, σ² is the population variance, and N is the population size.