National car rental systems inc.,commissioned the canadian automobile

Question 2

a)      [20 points] National Car Rental Systems Inc.,commissioned the Canadian Automobile Association (CAA) to conduct a survey of the general condition of the cars rented to the public by Hertz, Avis, National and Budget Rent-a Car. CAA officials evaluate each company’s cars using a demerit points system. Each car starts with a perfect score of 0 points and incurs demerit points for each discrepancy noted by the inspectors. One measure of the overall condition of a company’s cars is the mean of all scores received by the company (i.e., the company’s fleet mean score). To estimate the fleet mean score of each rental car company, 10 major airports were randomly selected and 10 cars from each company were randomly rented for inspection from each airport by CAA officials (i.e., a random sample of n = 100 cars from each company’s fleet was drawn and inspected).


                                 i.            [3 points] Describe the sampling distribution of , the mean score of a sample of n = 100 rental cars.      

                               ii.            [3 points] Interpret the mean of  in the context of this problem.           

                              iii.             [3 points] Assume that  and  for one rental car company. For this company, find .

                             iv.             [3 points] If  what is ?                             


                               v.            [4 points ] Refer to part iii. The company claims that their true fleet mean score “couldn’t possibly be as high as 30.” The sample mean score tabulated by the CAA for this company was 45. Does this result tend to support or refute the claim? Explain.

b)       [4 points] Will the sampling distribution of  always be approximately normally distributed? Explain.                     


Question 3

a)      [15 points]According to a recent Pew Internet and American Life Project Survey (October 2010), 67% of adults who use the Internet have paid to download music. In a random sample of n = 1,000 adults who use the Internet, let  represent the proportion who have paid to download music.

                                 i.            [4 points] Find the mean and standard deviation of the sampling distribution of .

                               ii.             [5 points] What does the Central Limit Theorem say about the shape of the sampling distribution of .

                              iii.            [3 points] What is the probability that less than 75% of adults who use the Internet have paid to download music?

                             iv.            [3 points] What is the probability that more than 50% of these adults have paid to download music?

b)           [5 points]Due to inaccuracies in drug-testing procedures (e.g., false positives and false negatives) in the medical field, the results of a drug test represent only one factor in a physician’s diagnosis. Yet, when Olympic athletes are tested for illegal drug use (i.e., doping), the results of a single positive test are used to ban the athlete from competition. In Chance (Spring 2004), University of Texas biostatisticians D. A. Berry and L. Chastain demonstrated the application of Baye’s Rule for making inferences about testosterone abuse among Olympic athletes. They used the following example: In a population of 1,000 athletes, suppose 100 are illegally using testosterone. Of the users, suppose 50 would test positive for testosterone. Of the nonusers, suppose 9 would test positive. If an athlete tests positive for testosterone, use Baye’s Rule to find the probability that the athlete is really doping.


Question 4

[15 points]Suppose that  and  are random observations taken from a population with mean  and variance. Consider the following three point estimators, X, Y, Z, of:

;  and .


a)      [5 points]  Show that all three estimators X, Y, and Z are unbiased estimators of .

b)      [5 points] Which of the estimators X, Y and Z is the most efficient? Explain.

c)       [5 points] Find the relative efficiency of X with respect to each of the other two estimators Y and Z.


Question 5

[20 points] The amount of time spent (in minutes) for the completion of the 4th assignment in Statistics by a random sample of 10 students gave the following results:  215, 182, 193, 208, 210, 176, 197, 188, 218, 213.  


a)      [5 points] Calculate the sample mean and sample standard deviation.


b)      [5 points] Specify the appropriate assumptions and find a 95% confidence interval for the population mean time spent by students on the 4th Assignment.


c)       [5 points] Find a 90% confidence interval for the population mean time spent by students on the 4th Assignment.

d)      [5 points] Compare your findings in (b) and (c).

Question 6

EXCEL problem.   (15 points)


a)      Simulate 10,000 draws from a standard normal distribution for each of 5 variables. Square each of these; you should have 5 columns, each of length 10000, with squared N(0,1’s) as entries. (Use Random Number Generator in Data Analysis.)


b)      Create a new column of length 10,000 by adding the five entries across each row and dividing this sum by 5.


c)      Sort the last column from low to high; use Rank and Percentile in Data Analysis. Using this sorted series, fill in the following Table as the answer to this problem, along with an EXCEL output of the first twenty rows of the six variables. Also, compute the average and variance of this last row to be included in the Table. Finally, include a histogram of the series as part of the output.


Simulation of the Chi-square Distribution (Χ5,α 2) with 5 Degrees of Freedom


Χ5,α 2

α  =  .99

α  =  .975

α  =   .95

α  =  .05

α  =  .025

α  =  .01

True Value

(from Χ2Tables)








Simulated Value










Simulated Mean



Simulated Variance





Essay Help
Calculate your paper price
Pages (550 words)
Approximate price: -

Why Work with Us

Top Quality and Well-Researched Papers

We always make sure that writers follow all your instructions precisely. You can choose your academic level: high school, college/university or professional, and we will assign a writer who has a respective degree.

Professional and Experienced Academic Writers

We have a team of professional writers with experience in academic and business writing. Many are native speakers and able to perform any task for which you need help.

Free Unlimited Revisions

If you think we missed something, send your order for a free revision. You have 10 days to submit the order for review after you have received the final document. You can do this yourself after logging into your personal account or by contacting our support.

Prompt Delivery and 100% Money-Back-Guarantee

All papers are always delivered on time. In case we need more time to master your paper, we may contact you regarding the deadline extension. In case you cannot provide us with more time, a 100% refund is guaranteed.

Original & Confidential

We use several writing tools checks to ensure that all documents you receive are free from plagiarism. Our editors carefully review all quotations in the text. We also promise maximum confidentiality in all of our services.

24/7 Customer Support

Our support agents are available 24 hours a day 7 days a week and committed to providing you with the best customer experience. Get in touch whenever you need any assistance.

Try it now!

Calculate the price of your order

Total price:

How it works?

Follow these simple steps to get your paper done

Place your order

Fill in the order form and provide all details of your assignment.

Proceed with the payment

Choose the payment system that suits you most.

Receive the final file

Once your paper is ready, we will email it to you.

Our Services

No need to work on your paper at night. Sleep tight, we will cover your back. We offer all kinds of writing services.


Essay Writing Service

No matter what kind of academic paper you need and how urgent you need it, you are welcome to choose your academic level and the type of your paper at an affordable price. We take care of all your paper needs and give a 24/7 customer care support system.


Admission Essays & Business Writing Help

An admission essay is an essay or other written statement by a candidate, often a potential student enrolling in a college, university, or graduate school. You can be rest assurred that through our service we will write the best admission essay for you.


Editing Support

Our academic writers and editors make the necessary changes to your paper so that it is polished. We also format your document by correctly quoting the sources and creating reference lists in the formats APA, Harvard, MLA, Chicago / Turabian.


Revision Support

If you think your paper could be improved, you can request a review. In this case, your paper will be checked by the writer or assigned to an editor. You can use this option as many times as you see fit. This is free because we want you to be completely satisfied with the service offered.