Exam (elaborations)
University of the People MATH 1281 self quiz 2 math 1281
- Course
- Institution
University of the People MATH 1281 self quiz 2 math 1281
[Show more]
Seller
Follow
Examhack
Reviews received
Content preview
In the book we compared two different estimators of the variance to eachother. 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.
m
The expectation of an observation is μ=5 and the variance is σ2 = 3. The next
er as
5 questions refer to the following R code that simulates the sampling
co
eH w
distribution of the two estimators:
o.
rs e
ou urc
o
aC s
vi y re
ed d
ar stu
is
Th
sh
Question 1
Not answered
Marked out of 1.00
Flag question
Question text
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/
, 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
Not answered
Marked out of 1.00
m
er as
Flag question
co
Question text
eH w
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
Question 3
Not answered
Marked out of 1.00
is
Flag question
Question text
Th
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/
The benefits of buying summaries with Stuvia:
Guaranteed quality through customer reviews
Stuvia customers have reviewed more than 700,000 summaries. This how you know that you are buying the best documents.
Quick and easy check-out
You can quickly pay through credit card or Stuvia-credit for the summaries. There is no membership needed.
Focus on what matters
Your fellow students write the study notes themselves, which is why the documents are always reliable and up-to-date. This ensures you quickly get to the core!
Frequently asked questions
What do I get when I buy this document?
You get a PDF, available immediately after your purchase. The purchased document is accessible anytime, anywhere and indefinitely through your profile.
Satisfaction guarantee: how does it work?
Our satisfaction guarantee ensures that you always find a study document that suits you well. You fill out a form, and our customer service team takes care of the rest.
Who am I buying these notes from?
Stuvia is a marketplace, so you are not buying this document from us, but from seller Examhack. Stuvia facilitates payment to the seller.
Will I be stuck with a subscription?
No, you only buy these notes for $12.49. You're not tied to anything after your purchase.
Can Stuvia be trusted?
4.6 stars on Google & Trustpilot (+1000 reviews)
82215 documents were sold in the last 30 days
Founded in 2010, the go-to place to buy study notes for 14 years now