Social Studies 201

Winter 2004

Problem Set 3

Due March 1, 2004

1.  Smoking and other vices.  Use the data from the midterm, in Table 1, to obtain the variance, standard deviation, and coefficient of relative variation for the rate of smoking per month and the rate of drinking per month.  From these measures, explain which of the two activities can be considered more variable.

Table 1.  Smoking and other vices.  Per cent of students reporting extent of smoking and drinking

 A. Rate of smoking/month B. Rate of drinking/month Response X Per cent Response X Per cent Didn’t smoke in last 30 days 0 76% Didn’t drink in last 30 days 0 23% 1-2 cigarettes per day 1.5 9% Only at special events 1 17% 3-9 cigarettes per day 6 8% 1-3 times 2 29% 10-24 cigarettes per day 17 6% 4-6 times 5 17% 25 or more 30 1% 7 or more times 10 14% Total 100% Total 100%

Source:  Social Studies 306, Social Attitudes and Personal Well-being, Fall 2003, University of Regina.

2.  Variation and patterns.  Use ssae98.sav to obtain the tables for this question.

a.       Use Analyze-Descriptive Statistics-Descriptives to obtain the mean and standard deviation of debt1 (student debt at the start of the semester), pay (hourly pay at job), and inc (family or household income).  From the data on the printout, calculate the range and coefficient of relative variation (CRV) for each variable.  From the range, standard deviation, and CRV, write a short note comparing the variability of these variables.

b.       Using Analyze-Compare Means-Means, obtain the means and standard deviations of V5 (increase corporate taxes), gpar (grade point average), and inc (household income) by future (evaluation of future – question 18 of survey).  Write a note comparing the statistics for the three variables (V5, gpar, and inc) for those with different evaluations of the future.

3.  Crosstabulations, variation, and probability.  Use ssae98.sav and Analyze-Descriptive Statistics-Crosstabs to obtain cross-classifications of (a) future by V5 and (b) future by gpar (grade point average).  Use these tables to answer the following questions.

A. Using the frequencies in the Worse off  column of the cross-classification of (a), calculate the standard deviation of V5.  Show your calculations.  The standard deviation should be the same as obtained in 2. b.

B. If an individual is randomly selected from the table of part (a), what is:

i.            The probability of selecting someone who believes they will be worse off?

ii.            The chance of selecting someone who disagrees (1 or 2) with increasing corporate taxes?

iii.            The likelihood of selecting someone who believes they will be better off and agrees (4 or 5) with increasing corporate taxes?

iv.            The probability of selecting someone who is neutral (3) on increasing corporate taxes or believes they will be about the same in the future?

v.            The probability of strongly agreeing with increasing corporate taxes given belief that they will be better off?  Given belief they will be worse off?

vi.            The probability of believing they will be better off given strongly disagreeing with increasing corporate taxes?  Given strongly agreeing with increasing corporate taxes?

vii.            Are the events of strongly agreeing with increasing corporate taxes and believing they will be worse off independent or dependent?

viii.            Are the events of being neutral (3) on increasing corporate taxes and believing they will be better off independent or dependent?

C.  If an individual is randomly selected from the table of part (b), obtain the following.

i.            The probability of obtaining a grade of 75 or above.

ii.            The probability of obtaining a grade of 75 or above and believing they will be worse off.

iii.            The conditional probability of a grade of 70-74, given belief they will be better off; given belief you will be about the same; and given belief you will be worse off.  Compare with the overall probability of obtaining a grade of 70-74 and comment on the independence or dependence of these events.

iv.            Are the events of a grade of 80 plus and the events of believing they will be better off independent or dependent?

D.  From the probabilities above, and perhaps using some of the information from question 2, does it appear that those with different evaluations of the future have different views on increasing corporate taxes or have different grade point averages?  Write a short note addressing this.

4. 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:

a.       Which approach to probability (theoretical, empirical, or subjective) is implied by likely in I?  By risk in II?  By risk in III?

b.       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.

c.       From III and comparing 15-17 and 12-14 year old boys, are the events of having an episode of depression and being a boy aged 15-17 independent or dependent?

d.       From I and II, what can you say about independence or dependence of the event of smoking and drinking and other events?