ST361: Ch 7.1 Estimation --- Point Estimation
Topics:
I. What is point estimation?
II. Criteria for evaluating point estimates
(a) unbiasedness
(b) small variability---small standard error
--------------------------------------------------------------------------------------------------------- Point Estimation = Use a single value to guess the unknown parameter

A point estimate is obtained by ________________________________________
________________________________________________________ , e.g.,
Parameter of interest
Statistic chosen to estimate
the parameter
Notation
Population mean
Population median
Population SD
Population proportion

The selected statistic is called the point estimator of the parameter, e.g.,

In this section we focus on the population mean assuming the population SD  is known
 How do we judge a good point estimator from a bad one?
(i)

(ii)



(iii)

(iv)
True 
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Criterion I: ___________________(i.e., on average, our guess is right on the target)
An estimator is unbiased if __________________________________________
Ex. Use X to estimate the parameter  (population mean). Is X unbiased?
Criterion II: ______________________ (i.e., for the uncertainty of our guess, the smaller the
better). So,
Ex. We wish to estimate population mean cost (denoted by  ) that a person spend on
groceries, and assume that the distribution of such cost is not symmetric. Person A
reported the sample mean based on a sample of size 10, person B reported the
sample mean based on a sample of size 100, and person C report the sample median
based on a sample size of 100. Whose estimate is the best?
 Note: Should also report the SE of the point estimate besides the estimate itself. It tells the
precision.
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Ex. A simple random sample of 10 students is selected from College A. For the 10 students, the number of
days each was absent during the last semester was to be (sorted from the smallest to the largest)
0, 1, 2, 2, 2, 2, 3, 5, 6, and 7
Note that
x
i
 30 and
x
2
i
 136 .
(a) Define  the mean number of absent days for the college’s students. Report an unbiased point
estimate for  .
(b) Explain why the point estimate in (a) is unbiased
(c) Report a point estimate for the SD of the absent days for the college, 
.
(d) Based on (c), report the S.E. of the point estimate in (a)
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