# 02 Estimators Flashcards

1

Q

a random sample can be used to…

A

…estimate the population mean

…test hypotheses about the population mean

…construct an confidence interval for the population mean

2

Q

estimator

A

a mathematical rule used to calculate an estimate

3

Q

unbiased estimator

A

E(^μy) − μy = 0

4

Q

consistent estimator

A

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.

5

Q

efficient estimator

A

var(^μy) < var(~μy)

6

Q

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

A

Y1 is unbiased and consistent, but not efficient.

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