Statistical Analysis (estimation, distribution, etc.)

Question 4

Let x₁, x₂, …xₓ be a random sample of n i.i.d. observations
following the Poisson distribution with parameter (mean) ϴ such that E(Xₐ) = ϴ.  Consider three estimators of ϴ given as:

ϴ₁ = X,     ϴ₂ = X₁,   ϴ₃ = (x₁ + 2x₂)/3

i.) 
Show that all the three estimators are unbiased

ii.) 
Calculate which of three has the least Variance

Question 5

A psychology researcher wants to find out if exercising
before taking a quiz affects a student’s performance.  To test this he randomly assigns students to
either exercise for 10 minutes before taking a short quiz, or to take the quiz
without exercising first.  37 students
exercise first and averaged 84% on the quiz with a standard deviation of 7%
while 32 students skip exercising and score 81% with a standard deviation of
6%.  Neither sample was substantially
skewed.

a.) 
Write down the null and the alternative
hypothesis in the test.

b.) 
Draw a picture of the samlpling distribution
assuming that the null hypothesis is true, shading in the regions(s) that would
result in a type 1 error (falsely rejecting the null hypothesis assuming that
it’s true of 0.05

c.) 
Test the hypothesis at 95% confidence.  NOTE: 
Instead of assuming that the variances are equal, first test for the
equality of variances.  Once you conclude
regarding the equality of variances, test for the equality of mean performance.

d.) 
What is the P-value of the test?

Question 6

a.) 
For the IND ENG 716 group project, members of
group 5 needed to determine if the percentage titanium content std. dev. In an aerospace
casting is within the acceptable specifications of SD = .30.  To do this, they tested the percentage
content of titanium in 51 casting specimen and the sample std. dev. was 0.37.  Construct the 95% confidence interval of the
standard deviation and comment on whether the company’s castings are within the
allowable specifications

b.) 
Next the group needed to study if the two ally
impurity level detection tests that the company uses perform the same.  To do this, they tested eight specimens on
both apparatus and recorded the following impurity levels:

Is there evidence at 90% confidence that
the tests differ in mean impurity levels? 
Hint:  be careful to decide if
these are homogenous samples or not, hence use the appropriate test.  What is the P-value of your test?

Specimen

Test 1

Test 2

1

1.2

2.0

2

1.3

1.7

3

1.5

1.5

4

1.4

1.3

5

1.7

2.0

6

1.8

2.1

7

1.4

1.7

8

1.0

1.6

Calculate the price of your order

550 words
We'll send you the first draft for approval by September 11, 2018 at 10:52 AM
Total price:
$26
The price is based on these factors:
Academic level
Number of pages
Urgency
Basic features
  • Free title page and bibliography
  • Unlimited revisions
  • Plagiarism-free guarantee
  • Money-back guarantee
  • 24/7 support
On-demand options
  • Writer’s samples
  • Part-by-part delivery
  • Overnight delivery
  • Copies of used sources
  • Expert Proofreading
Paper format
  • 275 words per page
  • 12 pt Arial/Times New Roman
  • Double line spacing
  • Any citation style (APA, MLA, Chicago/Turabian, Harvard)

Our guarantees

Delivering a high-quality product at a reasonable price is not enough anymore.
That’s why we have developed 5 beneficial guarantees that will make your experience with our service enjoyable, easy, and safe.

Money-back guarantee

You have to be 100% sure of the quality of your product to give a money-back guarantee. This describes us perfectly. Make sure that this guarantee is totally transparent.

Read more

Zero-plagiarism guarantee

Each paper is composed from scratch, according to your instructions. It is then checked by our plagiarism-detection software. There is no gap where plagiarism could squeeze in.

Read more

Free-revision policy

Thanks to our free revisions, there is no way for you to be unsatisfied. We will work on your paper until you are completely happy with the result.

Read more

Privacy policy

Your email is safe, as we store it according to international data protection rules. Your bank details are secure, as we use only reliable payment systems.

Read more

Fair-cooperation guarantee

By sending us your money, you buy the service we provide. Check out our terms and conditions if you prefer business talks to be laid out in official language.

Read more
error: Content is protected !!