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# Chapter 10 Notes.docx

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Operations Management and Information System
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OMIS 2010
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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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Description
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
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