University of the People MATH 1281 self quiz 2 math 1281

In the book we compared two different estimators of the variance to each
other. One estimator was the sample variance S2, an unbiased estimator of
the variance. This estimator was computed using the function " var ", which
involves dividing the sum of squared deviations from the average by the
number of observations minus 1 (n-1). The alternative estimator was
obtained by dividing the sum of squares by the number of observations ( n ).
This alternative estimator was equal to [(n-1)/n]S2.
In this exercise we compare two estimators of the standard deviation that
are derived from the estimators of the variance. The first is S, the square root
of S2, and the second is the square root of the alternative estimator of the
variance. The first estimator of the standard deviation may be computed
with the function " sd ". The alternative estimator may be computed by the
multiplying the first estimator by √ [(n-1)/n].
We consider the bias, variance and mean square error of both estimators of
the standard deviation. We assume a Normal sample of n=20 observations.




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The expectation of an observation is μ=5 and the variance is σ2 = 3. The next




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5 questions refer to the following R code that simulates the sampling




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distribution of the two estimators:




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rs e
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o
aC s
vi y re
ed d
ar stu
is
Th
sh




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, In the context of the simulation, the value of the parameter that is being
estimated is: (Choose the number closest to the answer)
Select one:
a. 1.71
b. 3.00
c. 1.73
d. 1.69
Feedback
The variance of the measurement is equal to 3. The standard deviation, the
value that is being estimated, is equal to √ 3 = 1.732051. After rounding up
we obtain 1.73 as the solution.
The correct answer is: 1.73
Question 2
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The bias of the first estimator of the standard deviation is: (Choose the




o.
number closest to the answer)
Select one: rs e
ou urc
a. 1.71
b. -0.023
c. 1.73
o

d. 0.00
aC s
vi y re


Feedback
The bias of the first estimator is the difference between its expectation,
1.708774, and the value of the estimated parameter, √ 3. The difference is
equal to -0.02327681 ≅ -0.023.
ed d




The correct answer is: -0.023
ar stu




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is




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The bias of the alternative estimator of the standard deviation is: (Choose
the number closest to the answer)
Select one:
sh




a. 1.71
b. -0.023
c. 1.73
d. -0.067
Feedback


This study source was downloaded by 100000831788613 from CourseHero.com on 09-23-2021 04:59:16 GMT -05:00


https://www.coursehero.com/file/37702999/self-quiz-2-math-1281docx/