Social Studies 201

Second Midterm Examination

10:30 – 11:20 a.m., November 5, 2003

Answer any three (3) of the following five questions.   Each question has equal value.

1. Use of internet.  Using the data in Table 1, obtain the standard deviation and coefficient of relative variation for each of the variables (a) number of times used internet in last month, and (b) number of hours used internet in past week.  Using these statistics, briefly comment on the variability of these two variables in this sample.

2. Health status and household income.  Regarding the 861 cases in Table 3 as a population from which a random sample of size one is drawn, answer the following.

a.       What is the probability of selecting a respondent who has fair health status and has an income of \$20,000 or more?

b.      What is the probability of selecting a respondent who has poor health status or is from the lowest income group?

c.       Are the events of being from the middle-income group and having good health status independent or dependent?  Explain.

d.      Are the events of being in the lowest income group and having excellent health status independent of dependent?  Explain.

e.       From c. and d. and by examining Table 3 (and possibly with the help of Table 4), briefly comment on whether there is any connection between health status and household income?

3. Variation in health status by income level.  From Table 3, compute the standard deviation of health status for (a) those from the lowest household income group and (b) those from the highest household income group.  (Use the values 1-5 for health status, as shown in the table).  By referring to the frequency distributions of the columns of Table 3 (or the percentage distributions of Table 4), explain why the standard deviations differ in the way they do.

4. Distribution of income.  The distribution of household income for Saskatchewan respondents has a mean of fifty thousand dollars and a standard deviation of thirty-five thousand dollars.  Using these values, and assuming that household income is normally distributed, obtain the following.

a.       Proportion of households with incomes below \$10,000.

b.      Percentage of households with incomes above \$100,000.

c.       Proportion of households with income between \$30,000 and \$80,000.

d.      Proportion of households with income between \$10,000 and \$30,000.

e.       Compare the results of a. – d. with the actual distribution of household income in Table 2, commenting on whether household income in Saskatchewan appears normally distributed.

5. Adolescent self-perception of health.   On October 31, 2003, Statistics Canada released a report “Factors related to adolescents’ self-perceived health.”  The data for the report came from a survey of 12,715 adolescents aged 12 to 17.  The following three statements come from the report.

I.  Adolescents who considered their own health to be poor, fair or good were more likely to smoke, drink or be obese.

II.  Knowledge of risks don’t prevent smoking and drinking.

III.  Nearly 6% of 12- to 14-year-old girls had a high risk of having a major depressive episode in the year before the survey, compared with 2% of boys the same age.  Among 15- to 17-year-olds, the proportion of girls who had such an episode was much higher (11%).  By contrast, 15- to 17-year-old boys were no more at risk of depression than those aged 12 to 14.

Answer the following using these three statements.

1. From III, what are the conditional probabilities of having a major depressive episode, given (i) event of being a 12- to 14-year-old girl and (ii) event of being a 12- to 14-year-old boy?   From this, what can you say about independence or dependence of events.
2. From III, are the events of having an episode of depression and being a boy aged 15-17 independent or dependent?
3. From I and II, what can you say about independence or dependence of the event of smoking and drinking and other events.
4. Which approach to probability (theoretical, empirical, or subjective) is implied by likely in I?  By risk in II?

The data in Tables 1-4 come from Saskatchewan respondents surveyed in Statistics Canada, 2000 General Social Survey, Cycle 14: Access to and Use of Information Communication Technology

# Table 1.  Use of internet in last month and past week, ten respondents

 Identification number Number of times used internet in last month Number of hours used internet in past week 1 30 3 2 12 4 3 28 10 4 30 22 5 27 7 6 3 1 7 6 1 8 15 2 9 10 2 10 27 10

Table 2. Frequency and percentage distribution of Saskatchewan household income

 Income in thousands of dollars Number of respondents Percentage of respondents 0 15 1.7 Less than 5 10 1.2 5-10 36 4.2 10-15 67 7.7 15-20 56 6.5 20-30 113 13.1 30-40 112 12.9 40-50 101 11.7 50-60 103 11.9 60-80 104 12.0 80-100 69 8.0 100 plus 79 9.1 Total 865 100.0

Table 3. Cross-classification of health status by household income

Number of respondents with each combination of characteristics

 Health status Household income Total Under \$20,000 \$20,000 to \$60,000 \$60,000 plus Poor (1) 11 5 1 17 Fair (2) 17 38 4 59 Good (3) 74 125 52 251 Very good (4) 58 155 120 333 Excellent (5) 20 106 75 201 Total 180 429 252 861

Table 4 presents column percentages for the data in Table 3.  While you need not use Table 4, you may find it helpful in answering questions 2 and 3.

Table 4. Column percentages for cross-classification of health status by household income of Table 3.  Percentage of column total

 Health status Household income Total Under \$20,000 \$20,000 to \$60,000 \$60,000 plus Poor (1) 6.1 1.2 0.4 2.0 Fair (2) 9.4 8.9 1.6 6.9 Good (3) 41.2 29.1 20.6 29.2 Very good (4) 32.2 36.1 47.6 38.6 Excellent (5) 11.1 24.7 29.8 23.3 Total 100.0 100.0 100.0 100.0