**Social Studies 201 – Fall 2000**

**Second Midterm Examination – 8:30 – 9:20 a.m.,
November 8, 2000**

**Answer
any three (3) questions**

** **

**1**. The following data come
from the article “Murder rate falls to level not seen since 1967” in *The Globe and Mail*, October 19, 2000, p.
A3. The data refer to Canada’s homicide
rate and number of homicides as reported to police during the 1990s.

Year |
Homicide rate per 100,000
population |
Number of homicides |

1990 |
2.38 |
660 |

1991 |
2.69 |
754 |

1992 |
2.58 |
732 |

1993 |
2.18 |
627 |

1994 |
2.05 |
596 |

1995 |
2.00 |
588 |

1996 |
2.14 |
635 |

1997 |
1.95 |
586 |

1998 |
1.84 |
558 |

1999 |
1.76 |
536 |

For the ten years, the mean annual homicide rate is 2.16 and the mean annual number of homicides is 627. Calculate the standard deviation and coefficient of relative variation for (i) the annual homicide rate and (ii) the annual number of homicides. Briefly explain which of the two series seems more varied.

**2**. From the 1996 Census of Canada, Saskatchewan males provided the
following data concerning their sources and amount of income.

Wages |
Investment Income |
||

Income (thousands of
dollars) |
Per Cent |
Income (thousands of
dollars) |
Per Cent |

0 |
36.0 |
0 |
66.3 |

0-20 |
18.9 |
0-2 |
19.4 |

20-40 |
24.1 |
2-4 |
4.9 |

40-60 |
14.2 |
4-10 |
5.3 |

60+ |
6.8 |
10+ |
4.1 |

Total |
100.0 |
Total |
100.0 |

For each of wages and investment income, calculate the standard deviation and coefficient of relative variation (for the open-ended intervals, assume a midpoint of $80 thousand for wages and $20 thousand for investment income). Briefly explain the differences in variation for the two distributions.

**3**. The 944 Saskatchewan respondents in Statistics Canada’s General
Social Survey, Cycle 11, 1996, reported a mean household income of $38 thousand
dollars, with a standard deviation of $27 thousand dollars.

a. Assuming that incomes are normally distributed, what is

(i) the proportion of households in the sample with an income of over $80,000?

(ii) the probability that the household has an income below $20,000, if that household is randomly selected from the sample?

(iii) the number of households in the sample with incomes between $30,000 and $50,000?

(iv) the 75^{th} percentile of
income?

b. The following table provides the income distribution for all 944 Saskatchewan households in the sample.

Household Income |
Number of Households |
Per Cent of Households |

less than $10,000 |
74 |
7.8 |

$10-20,000 |
212 |
22.5 |

$20-30,000 |
159 |
16.8 |

$30-40,000 |
154 |
16.3 |

$40-50,000 |
106 |
11.2 |

$50-60,000 |
84 |
8.9 |

$60-80,000 |
77 |
8.2 |

$80,000 plus |
78 |
8.3 |

Total |
944 |
100.0 |

From the above table and the results in part a., comment on how well the normal distribution fits the actual distribution of income of the sample of Saskatchewan households.

**4**. The following data come from the Saskatchewan respondents to
Statistics Canada’s General Social Survey, Cycle 11, 1996. The table shows the number of respondents by
household income, cross-classified by the number of cigarettes the respondent
smokes daily.

Number of Cigarettes Smoked Daily |
Household Income |
Total |
||

Less than $30,000 |
$30,000 – 60,000 |
$60,000 plus |
||

0 |
209 |
369 |
128 |
706 |

1-10 |
17 |
32 |
12 |
61 |

11-20 |
44 |
74 |
11 |
129 |

Over 20 |
15 |
23 |
4 |
42 |

Total |
285 |
498 |
155 |
938 |

a. If a respondent is randomly selected from this group of 938 Saskatchewan respondents, what is the probability that the respondent:

i. smokes more than 10 cigarettes daily?

ii. smokes more than 10 cigarettes daily given that the respondent is lower income (less than $30,000)?

iii. has income of under $30,000 given that the respondent smokes 11-20 cigarettes daily?

b. Are the following pairs of events independent or dependent?

i. does not smoke and is middle income ($30-60,000).

ii. smokes over 20 cigarettes daily and is from the highest income group.

c. “Lower income people are more likely to smoke.” Cite probabilities that either support or cast doubt on this statement.

**5**. a. If the table in question 4 is representative of all
Saskatchewan adults, approximately 25% of Saskatchewan adults smoke
cigarettes. If a random sample of 8
Saskatchewan adults is selected, use the normal approximation to the binomial to
estimate the probability that

i. less than 3 of those selected are smokers.

ii. 6 or more of those selected are smokers.

b. You walk by an office building in downtown Regina and you observe a group of 8 workers outside the building, each of them smoking. How do you explain this, in view of the probability in b?

**6**. The following table comes from *The
Globe and Mail* of November 3, 2000, pp. A1 and A8. The table shows the percentage distribution
of support for each political party in the six regions of Canada. The data were obtained by Ipsos-Reid/Globe
and Mail/CTV between October 27 and November 1, 2000. The poll represents a randomly selected sample of 2,500 adult
Canadians, asking them “Thinking of how you feel right now, if a federal
election were held tomorrow, which of the following parties’ candidates would
you, yourself, be most likely to support?”

Region |
Percentage supporting each political party |
Total |
|||||

Liberal |
Alliance |
Bloc Québecois |
NDP |
PC |
Other |
||

B.C. |
34 |
52 |
0 |
7 |
5 |
2 |
100 |

Alberta |
23 |
61 |
0 |
8 |
7 |
1 |
100 |

Man/Sk |
32 |
41 |
0 |
20 |
5 |
2 |
100 |

Ontario |
53 |
24 |
0 |
9 |
11 |
3 |
100 |

Quebec |
38 |
10 |
43 |
6 |
2 |
1 |
100 |

Atlantic |
50 |
15 |
0 |
10 |
24 |
1 |
100 |

Canada |
42 |
29 |
10 |
9 |
8 |
2 |
100 |

a. From this table, what is the probability that a randomly selected voter

i. supports the Alliance or Bloc?

ii. supports the Bloc, given that the respondent is from Alberta?

iii. supports the Alliance, given that the respondent is from the Atlantic region?

b. Identify one pair of events that are independent of each other and one pair of events that are dependent on each other.

c. *The
Globe and Mail *reports “The poll … suggests a starkly divided country, with
the Canadian Alliance handily winning the battle for the West but lacking
significant support east of Manitoba.”
Provide conditional probabilities that support this statement.