Ch 7

Question 1

Estimator

Answer 1

Random variable of population parameter depends on sample info

Question 2

Estimate

Answer 2

Specific value of random variable

Question 3

Point estimator (with example)

Answer 3

Function of sample info that produces single number called POINT ESTIMATE

Ex: sample mean X is point estimator of population mean µ

Question 4

Unbiased estimator

Answer 4

Point estimator Ø is said to be unbiased of population parameter Ø if E(Ø) = Ø

Question 5

Bias (equation)

Answer 5

Bias in Ø is defined as difference between mean and Ø (bias(Ø) = E(Ø) - Ø

Question 6

What is the bias of unbiased estimator?

Answer 6

0

Question 7

Most efficient estimator

Answer 7

If there are several unbiased estimators,unbiased estimator with smallest variance is most efficient estimator

Question 8

Properties of unbiased estimators Ø1 and Ø2

Answer 8

1. Ø1 is more efficient than Ø2 if Var(Ø1) < Var(Ø2)

2. Relative efficiency of Ø1 with respect to Ø2 is RATIO of their variances

Question 9

Relative efficiency

Answer 9

Var (Ø2) / Var (Ø1)

Question 10

Confidence interval estimator

Answer 10

Rule for determining an interval that is likely to include parameter

Question 11

Confidence interval of Ø (equation)

Answer 11

Interval from a to b when P(A < Ø < B) = 1 - a (a is between 0 and 1)

100(1 - a)%

Question 12

Confidence level

Answer 12

Quantity of 100(1 - a)%

Question 13

Width of confidence interval

Answer 13

W = 2(ME)

Question 14

Upper confidence limit (UCL)

Answer 14

UCL = X + ME

Question 15

Lower confidence limit (LCL)

Answer 15

LCL = X - ME

Question 16

If outliers heavily affect the population distribution…

Answer 16

Sample mean is less efficient than other estimators (such as median)

Question 17

As number of degrees of freedom increases for Students “t” distribution it becomes…

Answer 17

Increasingly similar to standard normal distribution