STA304H5F人工智能

STA304H5F: Surveys, Sampling and Observational Data
Assignment # 1
Instructions
Due Date: Thursday October 21, 20201 at 11:59 pm. Be sure to submit your work before it is
due. Late submissions will not be accepted.
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JPEG versions of your assignment answers. Upload your solution to crowdmark, one question at
a time.
Attempt all questions. However, not all questions are marked. The questions to be marked are not
announced ahead of time.
Solutions must be presented neatly, completely, and with logical flow. Do not skip steps in your
solutions or fail to describe what you are doing.
Solutions can be hand-written or typed.
With regard to remote learning and online courses: Students are expected to adhere to the Code of
Behaviour on Academic Matters regardless of the course delivery method. By offering students the
opportunity to learn remotely, it is expected that students will maintain the same academic honesty
and integrity that they would in a classroom setting. Potential academic offences in a digital context
include:

1. Accessing unauthorized resources (search engines, chat rooms, Reddit, tutoring service, etc.)
   for assessments.
2. Using technological aids (e.g. software) beyond what is listed as permitted in an assessment.
3. Posting test, essay, or exam questions to message boards or social media.
4. Creating, accessing, and sharing assessment questions and answers in virtual “course groups.”
5. Working collaboratively, in-person or online, with others on assessments that are expected to
   be completed individually.
   All suspected cases of academic dishonesty will be investigated following procedures outlined in the
   Code of Behaviour on Academic Matters. If you have questions or concerns about what constitutes
   appropriate academic behaviour or appropriate research and citation methods, you are expected to
   seek out additional information on academic integrity from your instructor or from other institutional
   resources.
   STA304H5 Fall 2021 Page 1 of 3
   Answer All the following questions.
   Question 1 Find a survey on one of the following websites: Survey.Net (www.survey.net), Statistics
   Canada (https://www.statcan.gc.ca/eng..., or Computing in the Humanities and Social
   Sciences (http://www.chass.utoronto.ca/).
   Answer the following questions regarding your selected survey.
   (a) Write one paragraph or two describing the survey (study).
   (b) What is/are the population, the sampling unit(s), the sampling frame(s), the sample size(s), and
   the parameter(s).
   (c) What is the sampling procedure being used? Explain.
   (d) Describe a possible source of bias in this study. Note: Comment on a bias that is certain to be
   present in this particular study. Do not comment on biases that might be present in any study.
   Question 2 Select only ONE of the following possible studies/projects:
   (1) The perception of students’ online learning experience during COVID-19 pandemic.
   (2) Undergraduate students’ attitudes toward statistics in online environment.
   (3) Fairness of Assessment in High-Educational Statistics/Mathematics Courses During COVID-19 Cri-
   sis.
   (4) The impact of COVID-19 on the students’ mental health.
   (5) Students’ satisfaction regarding university food court service.
   (6) Proportion of STA304 students who prefer Starbucks to Tim Hortons.
   (7) Proportion of Students from STA304 that take public transit to commute to UTM.
   (8) Proportion of STA304 students prefer to take online tutorial or attend real tutorial.
   Answer the following questions regarding your selected project.
   (a) What is/are the project title, the population, the sampling unit(s), the variable(s) of interest, and
   the parameter(s).
   (b) Describe the sampling frame and state how you will access the sampling frame or explain why you
   are not using a sampling frame.
   (c) What sampling procedure you would like to use? Explain.
   (d) Assume you would like to design a questionnaire, provide three main questions to be included in
   this questionnaire.
   (e) Describe a possible source of bias in this project. Note: Comment on a bias that is certain to be
   present in this particular project. Do not comment on biases that might be present in any study.
   STA304H5 Fall 2021 Page 2 of 3
   Question 3 Let y1, y2, · · · , yn be a simple random sample of size n. Assume that sampling is with
   replacement. Recall that

μ: the population mean, σ2: the population variance, and τ : population total.
(a) Show that E(s2) = σ2. That is, s2 is unbiased estimator of σ2.
(b) Can you conclude that s is unbiased estimator of σ Explain.
(c) Derive unbiased estimator of σ2yˉ, the variance of yˉ.
(d) Derive unbiased estimator of σ2τ , the variance of τ .
Question 4 Solve the following problems from the textbook: 4.27, 4.28, 4.41, and 4. 48.