QUESTION 1: Estimating p

In summer, 2016, Forum Research Inc. conducted a telephone survey of a random sampling of Canadian voters to find out if they were in favor of the expansion to the Canadian Pension Plan (CPP) proposed by the Liberal government. Of the 1,429 Canadian voters surveyed, 929 reported being in favor of a CPP expansion. Suppose for the purposes of this question it is reasonable to consider the 1,429 Canadians surveyed as a simple random sample (SRS) of all Canadian voters.

1. Compute the approximate 90% confidence interval for the true percentage of Canadian voters in favour of a CPP expansion. Be sure to check any necessary conditions and show your steps.
2. Suppose the true proportion of Canadian voters in favour of the proposed CPP expansion is actually 0.62. Use this information, as well as other relevant information provided in Question 2 above to answer these questions:

1. What is the approximate distribution of the sample proportion of Canadian voters in favour of the proposed CPP expansion? Be sure to show your steps.
2. If you were going to take another SRS of 1,429 Canadian voters, what is the probability that the sample proportion in favour of the proposed CPP expansion will be between the upper and lower limits of the interval you computed in Question 2, Part a? Be sure to show your steps.

c. Suppose Forum Research Inc. was hired to conduct another survey to find out the percentage of Ontario voters in favour of enhancements to Ontario Health Insurance (OHIP) coverage. How many Ontario voters are they going to have to randomly select to estimate the true percentage of Ontario voters in favour of OHIP enhancements within 5 percentage points, 19 times out of 20? Be sure to show your steps.

d. Suppose a more precise (i.e., narrower ) interval estimate for the true percentage of Canadian voters in favour of the proposed CPP expansion than the one calculated in Question 2, Part a, was needed. Which of the following strategies would decrease the margin of error? Select all that apply.

Question 2 : Interpreting a confidence interval

A simple random sample of children at a large school were asked, "During the past month, how many students have you known personally that were victims of cyber bullying?" 21.8% of the respondents knew between 3-5 victims. The 95% confidence interval for this percentage is 13.6% to 30.0%.  Use this information to answer Parts a and b of this question.

1. The following interpretation of this confidence interval is INCORRECT: There is a 95% probability that the true proportion of students who personally know between 3-5 victims of cyber bullying is between 13.6% to 30.0%. Explain why this interpretation is incorrect.
2. What is the correct interpretation of this confidence interval?

Question 3: Experiment Question

Researchers recruited 20 patients who experience regular muscle cramping to participate in a study evaluating the relationship between stress and muscle cramps. All subjects met in a classroom on campus one morning. The subjects knew they were participating in a study of muscle cramps, but were unaware of what they would be doing that morning. Half the subjects were randomly chosen to leave the room with a research assistant who took them to be exposed to increased stress by being placed into an elevator that fell rapidly and stopped abruptly and the other half were left at no or baseline stress in the classroom. All subjects were then asked to report whether or not they experienced muscle cramps within the next 6 hours. Once the data were collected, the results were compared for the two groups. Use this information to answer Parts a-e of this question.

1. What type of study is this?

   		Experiment
   		Observational Study

2. What is "being placed into an elevator that fell rapidly and stopped abruptly" in the context of this study? Select all that apply.

   		Response variable
   		Explanatory variable
   		Factor
   		Level
   		Treatment
   		Experimental unit
   		Block

3. What is ‘ whether or not a subject experienced muscle cramps within the next 6 hours’ in the context of this study? Select all that apply.

   		Response variable
   		Explanatory variable
   		Factor
   		Level
   		Treatment
   		Experimental unit
   		Block

4. What is ‘s tress level’ in the context of this study? Select all that apply.

   		Response variable
   		Explanatory variable
   		Factor
   		Level
   		Treatment
   		Experimental unit
   		Block

5. List the three fundamental principles of experimental design and indicate if (and if so, explain how) the researchers incorporated each of them into their design.

Question 4: Mall Survey

Administrators at a large shopping mall have noticed a big drop in shoppers at their mall so they decide to conduct a survey study to learn more about their shoppers and to find out how they can attract more shoppers. They plan to have two mall staff members stand at the main entrance of the mall for a full work week in December, 2016 (Monday-Friday, from 9am-5pm) to greet shoppers and to invite them to complete a short survey. The survey consists of demographic questions (e.g., age, gender), questions related to shopping habits (e.g., reason for visit to the mall, number of monthly visits to the mall, other places they shop in a typical month) as well as the following questions: "The mall invests a huge amount of our budget to ensure that there are a wide variety of high quality goods and services available to our shoppers. Do you think we do a good job of accomplishing this? What else can we do to attract shoppers?" Answer the following questions based on mall administrators’ plan.

1. Multiple-choice - What type of study is this? Experiment Observational Study
2. Multiple-choice – What is the planned sampling method?
   Simple random sampling
   Stratified sampling
   Cluster sampling
   Systematic sampling
   Convenience sampling
   Volunteer sampling
   Taking a census
3. i. What is the population in the context of this plan?
   ii. What is the sample in the context of this plan?
4. How may selection bias be an issue based on this plan? Describe the impact may it have on the results.
5. How may measurement bias be an issue based on this plan? Describe the impact may it have on the results.

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