School

York University
Department

Operations Management and Information System

Course Code

OMIS 2010

Professor

all

Chapter 10 Notes

Introduction to Estimation

Concepts of Estimation

- The objective is to determine the approximate value of a population partameter on the basis of

a sample statistic

- Eg the sample mean is used to estimate the population mean. Therefoe, the sample mean is the

estimator of the population mean. The value of the sample mean is the estimate

Point and Interval Estimators

- There are TWO ways the sample data is used to estimate the population parameter

1) Point Estimator- draws inferences about a population by estimating the value of an

unknown parameter using a single value or point (compute value of estimator, thatâ€™s the

estimate)

- Disadvantages to point estimator: estimate will be wrong (eg probability that a continuous

random variable will be equal to a number is 0. And that xbar is equal to mu is 0), we need to

know how close the estimator is to the parameter, large sample will produce better results but

point estimators donâ€™t reflect the large sample sizes

2) Interval Estimator- draws inferences about a population by estimating the value of an

unknown parameter using an interval

- Affected by sample size

- In general, we want to use statistics with the most desirable qualities

1) Unbiased estimator- of a population parameter, the expected value is equal to the

parameter. Therefore, on average, the sample statistic is equal to the parameter. (eg Xbar is

an unbiased estimator of mu: E(Xbar)=mu, E(Phat)= p, E(Xbar1-Xbar2)=mu1-mu2

2) Consistency- an unbiased estimator is said to be consistent if the difference between the

estimator and the parameter grows smaller as the sample size grows bigger. We use

variance to guage closeness (eg V(Xbar)= o^2/n, V(Phat)=p(1-p)/n

3) Relative Efficiency- if there are two unbiased estimators of a parameter, the one whose

variance is smaller is said to be relatively more efficient

Estimating the Population Mean when the Population Standard Deviation is Known

- Confidence interval estimator of mu: with repeated sampling from the population, the

proportion of values of Xbar includes the population mean mu is equal to 1-alpha

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