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**ADM2303 Assignment 4 Part II | Complete Solution**

- From Mathematics, Statistics

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**ADM2303 Assignment 4 Part II**

**Please do not forget to: (1) Complete your statement of Academic Integrity within the body of your solution (front or back); and (2) to submit a PDF of your type-written (i.e., not handwritten) solution/report (recall that a submission cannot be marked unless it is in PDF format). ** **A4-II will be marked out of a total of 23 marks.**

**Question 1 [3 points] Multiple Choice **

The Canadian Council on Foreign Affairs (CCFA) has hired you and another ADM2303 student to help conduct a national survey about the support in the general population for an extension to Canada’s military deployments in the Middle East. You have been allocated the Ottawa downtown area and need to select respondents for the survey.

**[I]. (1 point) **If you decide to go to the Rideau Centre and position yourselves by the two entrances to the Centre and ask every 20th shopper entering the mall, which of the following sampling techniques would best describe your method?

- simple random sampling
- stratified sampling
- systematic sampling
- cluster sampling
- multi-stage random sampling

The CCFA has decided to follow up their initial study with two related but more complex surveys, S1 and S2, and you were assigned to the team working in the Ottawa Center district. More specifically, you were asked to cover the Glebe neighborhood.

**[II]. (1 point)** The study coordinator has asked you to follow a cluster sampling technique when selecting respondents for the S1 survey. Which one of the following strategies would meet this requirement ?

- Select the first 10 homes you pass by as you enter the Glebe.
- Select every 5th house on each street in the neighborhood.
- Randomly choose two streets in the Glebe and ask the inhabitants of every home on these streets to fill out the survey.
- Randomly select single family and multi-family homes proportional to the number of such homes in the neighborhood, as reported by Stats Canada.
- None of the above.

**[III]** **(1 point) **The study coordinator has asked you to follow a stratified sampling technique when selecting respondents for the S2 survey. Which one of the following strategies would meet the requirement?

- Select the first 10 homes you pass by as you enter the Glebe.
- Select every 5th house on each street in the neighborhood.
- Randomly choose two streets in the Glebe and ask the inhabitants of every home on these streets to fill out the survey.
- Randomly select single family and multi-family homes proportional to the number of such homes in the neighborhood, as reported by Stats Canada.
- None of the above.

**Question 2 [3 points] **

The national survey of the Canadian Council on Foreign Affairs found that that 52% of the people interviewed support extending Canada’s military deployments in the Middle East. The survey had a very large number of respondents and it is estimated that 52% is a good approximation for the true population proportion who support extending the military mission. A smaller non-governmental organization, Citizens for Justice and Transparency (CJT) also conducted a simple random sampling of 1000 people in Ottawa and found that 48% of the respondents are in favour of extending the mission.

(a) (1 point) What is the sample proportion of those who support extending the mission in the survey conducted by the CJT?

(b) (2 points) Assuming that the proportion of Ottawa residents who support extending the mission is the same as the national one, what is the probability that the proportion found in surveys such as the one conducted by the CJT is as small, or smaller, than 0.48? Justify your answer.

**Question 3 [11 points] **

The study conducted by the Canadian Council on Foreign Affairs also asked the respondents questions about their income and found that the household income can be modeled as a Gaussian distribution with mean $73 200 and standard deviation $33 200.

**(2 points)**What percentage of households earn more than $100K? Show the answer graphically.

**(2 points)**Approximately 4% of all households were considered to be under the poverty line. Using this model, find the household income levels that would be considered under the poverty line.

**(2 points)**If a random sample of 10 households is selected from the population and is the average income of these 10 households, what can you say about the distribution of and its parameters?

**(2 points)**What is the chance that the average income of the 10 households will be greater than $100K?

**(3 points)**The CCFA is also fundraising to support their global access to information projects and hopes to persuade 900 households to donate 0.5% of their household income to the CCFA. Assuming that each of the 900 homes in the sample would indeed donate exactly 0.5% of their income, what is the probability that the total charitable revenue so collected would exceed $400K?

**Question 4 [6 points]**

Two players play a dice game. Each rolls a fair die and the object of the game is to score points by rolling a certain number (i.e., rolling a six scores a player 1 point, but anything else will give a score of zero). Each player rolls the die sixty times and records the proportion of sixes obtained. They repeat the process of rolling the die sixty times and recording the proportion of sixes obtained many times. At the end of the game the players make a histogram of their results.

**(1.5 points)**Where would you expect the center of the histogram to be? Explain.

**(1.5 points)**What is the standard deviation of the sampling distribution of the proportion of sixes?

**(1.5 points)**Describe the shape of the sampling distribution of . Justify your answer.

**(1.5 points)**The players decide to repeat the exercise rolling the die only 10 times each. What can you say about the shape of the sampling distribution of ? Justify your answer.

**ADM2303 Assignment 4 Part II | Complete Solution**

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- Submitted On 11 Apr, 2015 01:22:56

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