Social Studies 201 – Fall 2000

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

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 75th 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.