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% 
12
cigarettes per day 
1.5 
9% 
Only
at special events 
1 
17% 
39
cigarettes per day 
6 
8% 
13
times 
2 
29% 
1024
cigarettes per day 
17 
6% 
46
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 Wellbeing, Fall 2003, University of Regina.
2. Variation and patterns. Use ssae98.sav to obtain the tables for this
question.
a.
Use
AnalyzeDescriptive
StatisticsDescriptives 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
AnalyzeCompare MeansMeans, 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 AnalyzeDescriptive StatisticsCrosstabs
to obtain crossclassifications 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 crossclassification 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 7074, 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 7074 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
selfperception of health. On October 31, 2003,
Statistics Canada released a report “Factors related to adolescents’
selfperceived 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 14yearold 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
17yearolds, the proportion of girls who had such an episode was much higher
(11%). By contrast, 15 to 17yearold
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 14yearold girl and (ii) event of
being a 12 to 14year old boy? From
this, what can you say about independence or dependence of events.
c.
From
III and comparing 1517 and 1214 year old boys, are the events of having an
episode of depression and being a boy aged 1517 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?