CHAPTER 10 – ESTIMATION
Statistical inference is the process by which we
acquire information and draw conclusions about
Qualities desirable in estimators are unbiasedness, consistency and relative efficiency. populations from samples.
Unbiasedness an unbiased estimator of a population parameter is an estimator whose
Objective of estimation is to determine the
expected value is equal to that parameter. E(X) = µ approximate value of a population parameter on
Consistency – If the difference between the estimator and the parameter grows smaller
2 the basis of a sample statistic.
as the sample size grows larger. V(X) is σ /n Point estimators don’t get closer to the
Relative efficiency - If there are two unbiased estimators of a parameter, the one whose Width of the interval
variance is smaller is said to be relatively efficient.
The width of the confidence interval estimate is a
function of the population SD, confidence level and
Estimating µ when σ is known 1-a a a/2 Za/2 sample size.
0.90 0.10 0.05 1.645
Use confidence interval estimator Population SD
The probability 1 – α is the confidence level 0.95 0.05 0.025 1.96 Consider σ=75, interval estimate 370.16 ± 29.40
If confidence level is 1 – α=0.95, 0.98 0.02 0.01 2.33 Consider σ=150, interval estimate 370.16 ± 58.80
α/2=0.025, Z = Z = 1.96 0.99 0.01 0.005 2.575 Confidence level
Consider 95%, interval estimate 370.16 ± 29.40
Error of estimation Consider 90%, interval estimate 370.16 ± 24.68
Sampling error as the difference between an estimator and parameter. Difference of X- µ Sample size
Bound on the error of estimation Consider n=25, interval estimate 370.16 ± 29.40
Consider n=100, interval estimate 370.16 ± 14.70
CHAPTER 11 – HYPOTHESIS TESTING
Null hypothesis is H (not enough evidence to infer H not rejecting null) A Type I error occurs when we reject a true null hypothesis. α