Point Estimates & Sampling

Question 1

For a sample of a independent, normal random variables from a population, how is the population mean and variance estimated?

Answer 1

Mean(pop) = (mean1+mean2+...)/n
Variance(pop) = var/n

Question 2

For a large sample size of a population, what probability standardised variable should be used for a one-sided test? What theorem is this?

Answer 2

Sampling distribution approx normal; Central Value Theorem

Z = [mean(sample)-mean(pop)]/(stdev./sqrt(n))

Question 3

When is the central value theorem applicable?

Answer 3

When n>30

Question 4

How can the central value theorem be applied for the difference between 2 sample means?

Answer 4

Z = [samp.mean1-samp.mean2-(pop.mean-pop.mean2)]/sqrt(var1/n1 + var2/n2)

Question 5

Why are point estimates used?

Answer 5

To seek an individual number based on sample data that isn’t dependent on random variables in the sample.

Question 6

What are the notation used for the point estimates for the mean, variance and proportion for a sample?

Answer 6

Mean = mu(hat) = samp.mean
Variance = signma^2(hat) = stdev.^2
Proportion = p(hat) = x/n

Question 7

Write the unbiased estimator statistic.

Answer 7

E(point estimate of parameter) - pop.parameter = 0

Question 8

Write the standard error of the sample mean if population variance is known.

Answer 8

sigmax = sigma/sqrt(n)

Question 9

Write the estimated standard error of the sample mean when population variance is not known.

Answer 9

sigmax(hat) = s/sqrt(n)