Chapter 10 Introduction To Estimation

Question 1

Objective of estimation

Answer 1

To determine the approximate value of a population parameter on the basis of a sample statistic

Question 2

Point estimator

Answer 2

Draws inferences about a population by estimating the value of an unknown parameter using a single value or point. (when we consider the calculated sample statistic to be the estimated population parameter)

Drawbacks:

• virtually certain to be wrong (probability of a continuous random variable = specific value =0)
• often need to know how close estimator is to parameter
• no way to reflect effects of larger sample size

Question 3

Interval estimator

Answer 3

Draws inferences about a population by estimating the value of an unknown parameter using an interval

• affected by sample size

Question 4

Desirable qualities of sample statistics

Answer 4

Unbiasedness
Consistency
Relative efficiency

Question 5

Unbiased estimator

Answer 5

An estimator of a population parameter whose expected value is equal to that parameter

(Average value of estimator taken from infinite samples = parameter. Or. On average the sample statistic = the parameter)

Question 6

Consistency

Answer 6

An estimator is consistent when the difference between the estimator and the parameters grows smaller as the sample size grows larger

Gauged using variance/standard deviation

Question 7

Relative efficiency

Answer 7

When there are two unbiased estimator of a parameter, the one whose variance is smaller is said to have relative efficiency

For normal population sample mean has a smaller variance than sample median and so is a relatively more efficient estimator.

Question 8

Central limit theorem

Answer 8

The mean of X is normally distributed if X is normally distributed, or approximately normally distributed if X is non-normal but n (sample size) is sufficiently large

Question 9

Interpreting confidence interval

Answer 9

There is a 1-a probability that the sample mean will be equal to a value such that the interval (mean x - z(a/2)(standard deviation/sq root sample #) to (mean x + z(a/2)(standard deviation/sq root sample #) will include the population mean

Confidence interval = percent of repeated samplings for which the above will be true

Question 10

Width of the confidence interval

Answer 10

Function of the population standard deviation, the confidence level, and the sample size

Higher level of deviation = wider interval

Decreased confidence level= narrower interval (95% standard)

Increasing sample size narrows interval but increases costs

Question 11

Confidence interval estimator of population mean

Answer 11

Sample mean + or - z(a/2)*(standard deviation / square root of n)

+ Gives upper confidence limit
- gives lower confidence limit

Question 12

Confidence level

Answer 12

Probability 1-a

Can use table to find z(a/2) value but

Confidence level / Z(a/2)
.90 / 1.645
.95 / 1.86
.98 / 2.33
.99 / 2.575