First
Midterm Examination
10:30 –
11:20, Friday, October 3, 2003
Answer
any three (3) of the six questions.
Each question has equal value.
The tables and figures are on the other page handed out.
1. Averages and percentiles.
a. While the word average is not contained in the following two newspaper headlines, each could be taken to imply one of the mode, median, or mean. For each headline, state which of the three concepts is relevant and explain why.
We’re worth $3.9 trillion: $121,900 for each Canadian. Leader-Post, September 27, 2003, p. B4.
Witness says Thatcher no risk to most people. Moose Jaw Times-Herald, September 26, 2003, p. 1.
b. The Leader-Post of September 30, 2003, on p. A1, reports on the coldest, warmest, windiest and wettest cities of Canada. Explain what percentile of dryness is implied for (i) Saskatoon and (ii) Regina in the following:
… the report says only six cities out of the 100 studied are drier and Saskatoon and only 11 are drier than Regina.
2. Teenage smoking. The data in Table 1 come from the Youth Smoking Survey conducted by Statistics Canada in 1994. All twenty-three teenagers in the sample of Table 1 reported being regular smokers. From these data,
a. What is the mode and mean of age first started smoking for (i) females and (ii) males?
b. Obtain the median number of cigarettes smoked daily for (i) females and (ii) males.
c. A researcher who has studied teenage smoking argues that smokers who began smoking at a younger age tend to smoke more than those who started later. Comment on this using the measures of central tendency in (a) and (b) and the data in Table 1.
3. Internet use. The bar charts of Figures 1 and 2 come from the Statistics Canada publication Canadian Social Trends, Summer 2002. From these figures, explain or show which of the following are correct statements.
a. For infrequent users, the mode is the category of 1-4 years.
b. For infrequent users, the median is in the category of 1-4 years.
b. The mean for infrequent users is approximately two years less than the mean for regular users.
4. Same-sex marriages. Table 2 contains the frequency distributions of responses for Edmonton and for southern Alberta residents in a July 2003 survey of Albertans. The survey was conducted by the polling agency Ipsos-Reid and asked respondents to state their opinion on the question “In general, do you support or oppose same-sex couples being allowed to marry and register their marriage with their provincial government? Do you strongly support, somewhat support, somewhat oppose or strongly oppose?” Using these data
a. What is the mode and median opinion for each region of Alberta. Which region expresses greater support for same-sex marriage?
b. Using the numbers in brackets in Table 2, what is the mean opinion for Edmonton?
5. Variables. Explain what is the highest level of scale each of the following variables has (nominal, ordinal, interval, or ratio). Also explain whether each is continuous or discrete.
a. Opinion about same-sex marriage (Table 2).
b. Region of Alberta (Table 2).
c. Number of cigarettes smoked daily (Table 1).
d. Length of time using internet (Figure 1).
6. Percentiles and mean.
a. From Figure 2, for regular users of the internet, calculate the eightieth percentile of length of time using internet.
b. From Table 1 and the note below the table, estimate the mean number of cigarettes smoked daily for each of males and females.
Table 1. Smoking behaviour of
twelve female and eleven male teenage smokers: Age started smoking and Number
of cigarettes smoked daily (see note below table)
|
Females |
Males |
||||
|
ID number |
Age of respondent |
Number smoked* |
ID number |
Age of respondent |
Number smoked* |
|
1 |
14 |
2 |
13 |
17 |
3 |
|
2 |
16 |
3 |
14 |
12 |
3 |
|
3 |
16 |
2 |
15 |
15 |
3 |
|
4 |
16 |
1 |
16 |
16 |
2 |
|
5 |
15 |
1 |
17 |
16 |
2 |
|
6 |
17 |
3 |
18 |
15 |
2 |
|
7 |
13 |
2 |
19 |
16 |
5 |
|
8 |
15 |
2 |
20 |
16 |
6 |
|
9 |
13 |
1 |
21 |
18 |
2 |
|
10 |
16 |
1 |
22 |
15 |
5 |
|
11 |
11 |
5 |
23 |
15 |
2 |
|
12 |
14 |
2 |
|
|
|
*Note: The values of “Number smoked” are as follows:
|
1 |
5 or less |
|
2 |
6-10 |
|
3 |
11-15 |
|
4 |
16-20 |
|
5 |
21-25 |
|
6 |
More than 25 |
Table 2. Opinions on same-sex marriage and registration, number of
respondents with each opinion in two regions of Alberta
|
Opinion on same-sex marriage |
Number in each region of Alberta |
|
|
Edmonton |
Southern Alberta |
|
|
Strongly support (1) |
56 |
10 |
|
Somewhat support (2) |
56 |
18 |
|
Somewhat oppose (3) |
38 |
11 |
|
Strongly oppose (4) |
117 |
46 |
|
Total |
267 |
85 |