PART A: MULTIPLE CHOICE (one (1) mark for each question)

For questions 1 to 5, select the best answer.

1. The number of nurses in Canada in 2007 was 330 000 and the population was 33 100 000. What is the per capita value for this situation?

A 0.01 B 100.30

C 32 770 000 D 33 430 000

• The Consumer Price Index (CPI) was 113.3 in December 2008. What does this mean if 2002 = 100?

A Overall, consumer prices decreased from 2002 to December 2008.

B Consumer prices in December 2008 were 113.3 times as great as prices in 2002. C The overall percent change in consumer prices from 2002 to December 2008

was 13.3%.

D The average consumer spent \$113.30 on goods and services per day inDecember 2008.

• Which is an example of response bias?

A A survey is mailed to 10 000 residents of each province in Canada. B A survey question asks, “Have you ever committed a crime?”

C A survey was mailed to 5000 rural residents of Ontario but only about 5%responded.

D Two students measured the time required to run across a field using twowristwatches. The recorded time was inaccurate because the wristwatches were not synchronized.

MAP4C:  Grade 12, Foundations for College Mathematics

• “In a recent study, 65% of city residents support increased spending on recreation. The study is accurate to within 3.1 percentage points, 19 times out of 20.” What does this mean?

A If this study were repeated 20 times, between 61.9% and 68.1% of respondentswould support increased spending on recreation in only the first 19 surveys.

B If this study were repeated numerous times, then between 61.9% and 68.1% ofrespondents would support increased spending on recreation in 95% of those studies.

C The pollsters asked 20 people and between 18 and 20 people said they wouldsupport increased spending on recreation 65% of the time.

D The survey was done 20 times and in

19 surveys, between 3.1% and 65% of respondents supported increased spending on recreation.

• Which situation contains sampling bias?

A A teacher writes the names of her 25 students on slips of paper, places them intoa box, and randomly chooses ten names.

B 150 000 Canadian residents were chosen for a survey by randomly selectingresidents from each province, in proportion to the population of each province.

C Every resident in Canada was asked to complete a questionnaire or a personalinterview for the 2006 Census of Canada.

D To determine Canadians’ views on global issues, a news reporter interviewedfive pedestrians.

PART B: FULL SOLUTION: For the following questions, show your all work in the space provided. If you are using the TVM solver, you must write in your solutions the value that you are entering into the calculator.

• The marks, out of 100, on an English assignment are shown in the table.

Determine Sydney’s percentile rank.  (3 marks)

MAP4C:  Grade 12, Foundations for College Mathematics

• The New Housing Price Index (NHPI) follows Canadian contractors’ selling prices of new residential houses. The index takes into account both the land and house selling price. The graph shows the value of the index from 1997 to 2007, (1997 = 100).

Source: Statistics Canada, CANSIM Table 327-

0005 Database: E-STAT

1. What is meant by 1997 = 100?  (1 mark)
• By what percent did the selling price of new residential homes increase from 1997 to 2007? (2 marks)
• By what percent did the selling price of new residential homes increase from 2006 to 2007? (2 marks)
• Would the graph distort the data if the vertical scale started at 90 instead of 0? Explain. (2 marks)

MAP4C:  Grade 12, Foundations for College Mathematics

• Identify and describe the bias in each situation. ( 2 marks each 8 marks total)
1. A citywide survey about parks and walking trails was sent to randomly selected households. The response rate was significantly higher for residents who had lived in the city for more than two years than residents who had lived in the city for less than two years.
• Warren did a project on ocean travel and recorded the units of the distance travelled by boats using an abbreviated form “nm” instead of using “nautical miles.” A student who read the report later mistook “nm” for “nanometres.”
• A pollster in front of a bank randomly selects people walking past to interview about saving money.
• A survey question asks, “Don’t you agree that students would greatly benefit if tuition fees were lowered?”

MAP4C:  Grade 12, Foundations for College Mathematics

• This graph was included in a newspaper article about home heating options.

(3 marks)

203-0019 Database: E-STAT

• What would be a better headline for the article?
• A 2007 article on identify theft included the statement: “Electronic payments boosted the Canadian economy by 25 per cent over the past two decades, representing \$107 billion of the economy’s \$437-billion growth from 1983 to 2003, according to a study sponsored by Visa Canada in 2004.” Identify three items of concern that would be part of a critical analysis. (3 marks)

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