02 Estimators

Question 1

a random sample can be used to…

Answer 1

…estimate the population mean
…test hypotheses about the population mean
…construct an confidence interval for the population mean

Question 2

estimator

Answer 2

a mathematical rule used to calculate an estimate

Question 3

unbiased estimator

Answer 3

E(^μy) − μy = 0

Question 4

consistent estimator

Answer 4

ˆμy p→ μy

The estimator is consistent if the probability that ˆμy is in the range (μy − c) to (μy + c) becomes arbitrarily close to 1 as n increases for any constant c > 0.

Question 5

efficient estimator

Answer 5

var(^μy) < var(~μy)

Question 6

Is Y1 an unbiased, consistent and/or efficient estimator for the population mean?

Answer 6

Y1 is unbiased and consistent, but not efficient.

var(Y1) = σ^2 > var(\bar{Y}) = σ^2 / n