Spring-Summer 2021
Mid-term test
Sampling and Surveys/MAT3377
MATH数学代写 This exam is open book and should be completed at home independently. The solution to this exam should be submitted on line…
• This exam is open book and should be completed at home independently.
• The solution to this exam should be submitted on line in brightspace. I strongly suggest to print the exam and complete it. Please keep the order of questions as it is provided. I prefer to see the questions and its solution in the same page. You can also use your ipad or any other tablet co complete this test and submit in one single p.d.f. file. Make sure to use a thick pen so that the scan or photos of your solution is legible. You are not allowed to consult with any other individuals during the time you write this exam. The submitted midterm should be in one single pdf file.
• Any conduct constitute cheating, misrepresenting, or unfairness including unauthorized aids and assistance, impersonating another person and committing plagiarism will be reported and will be dealt with based on regulations on code of conduct in academic matters. I will choose few students to conduct an interview about this exam.
• At the end of the exam you need to submit the test to brightspace. MATH数学代写
• If you are registered with SASS, please submit your exam to brighspace as well. You may add the additional time given to you. You should email me the document confirming the extra time after the exam. Remove personal health information and your private details before emailing the document to me.
• Where it is possible to check your work, do so.
• If you see any error in this exam, please report it on the first page of your exam.
• If a formula was proved in the lecture slides you do not need to prove it again. You can simply refer to page number in the lecture slides.
• You can use R if it is needed.
1. A typed book consists of N=800 pages. A simple random sample of 12 pages are taken and the number of typographical errors in each page are counted. The following data values are observed:
3, 4, 4, 2, 0, 8, 2, 1, 1, 2, 3, 3
[18] (i) Estimate the proportion of pages of this book with less than 3 errors and place a bound on your estimate.
[18] (ii) Estimate the total number of typographical errors in this book and place a bound on your estimate.
2. [18] In a stratified sampling with two strata and the cost function MATH数学代写
we have
With a total cost of $12000 how many sample can we draw in this case (use the optimum allocation). Calculate the sample sizes required from
both strata.
3. [18] Two hundred (n = 200) residents of a city of N=150,000 people (75,000 mlaes and 75,000 females) in the city were asked whether they are
in favor of increasing property taxes for the betterment of extracurricular activities in the schools. From 110 male in the sample only 50 were in favor
of raising the property taxes while out of 90 female in the sample 63 were in favor of raising taxes. Estimate the proportion of residents who are in
favor of the tax increase and place a bound on your estimate.
4. [20] Consider in a course offering for a graduate course only N = 5 students are registered.. After a test the scores for all 5 students are listed below:
85, 88, 98, 75, 70
A sample of size n = 2 is drawn at random without replacement (S.R.S.) to estimate the actual proportion (P) of students who score above 80. List
all the possible S.R.S. (all 
= 10 simple random samples) and in each case estimate P, the proportion of students who score above 80.
Use your list of all the 10 samples samples to show E(Pˆ) = P. Find Var(Pˆ) using the list of these 10 simple random samples. Moreover, use your list of all 10 samples to show
where Q = 1 − P.
5. [8] Find a formula for Var
where MATH数学代写
is the estimator for the population mean in a stratified sampling when sampling from each stratum is drawn with replacement. Use the same notations we used in this course.
