| December 14, 200
Sociology 2080 Statistics for Sociologists |
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1. In one UNC dormitory, the expected number of votes for Gore for the women in the dorm, E{X}, was 250 and for their mothers, E{Y}, it was 200. The signma2 {X} was 49 and sigma2{Y} was 36. The covariance, sigma{X,Y}, in the votes of these women was 30. (a.) What is the expected number of votes for Gore from these families?
(b) What is the variance of this total?
(c) What is the correlation of the votes of the college women and their mothers? What does this say about voting patterns of mothers and daughters?
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| 2. Two presidential candidates are contesting
election results from a southern state. Let's call them George and Al.
One, George, has a certified lead of 538 votes. The other candidate, Al,
hires you as a statistical consultant. You examine data from exit polling
of 10,000 people. On the basis of this sample, you estimates that Al would
gain, on average, 573 votes from a hand recount, with a variance in the
number of votes = 60. Would you say that it was very probable that Al would
win if a recount were allowed and urge him to continue to push for this?
You want to be pretty confident in what you tell Al, say 95% certain.
(a) What would be your null and alternative
hypotheses?
(b) What is the region of rejection?
(c) What is the value of the test statistic?
(d) What is your conclusion about the election
results with a recount?
(e) What assumptions did you have to make
to do this test?
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3. You send your undergraduate methods
students out to do a survey of gun ownership. You know from national data
that the probability of gun ownership is as follows:
Your 10 students go out and independently ask one person they meet whether s/he owns a gun. (a) On the basis of what you know from
the national data, how many gun owners would you expect to find in the
students' study?
(b) What would be the variance?
(c) What would be the probability of finding that 6 or 7 of the 10 respondents were gun owners? Write out the equations you would use and
calculate the number, then check the result from the tables.
(d) What does the probability distribution
of number of gun owners out of 10 look like (graphically)?
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| 4. Do women feel less successful in their
work lives than men? You ask the question, "How successful are you in your
work life," with 5 possible responses:
1=not at all successful 2=not very successful 3=somewhat successful 4=very successful 5=completely successful. Your results from your survey are:
(a) What would be your null and alternative
hypotheses?
(b) What is the value of your test statistic?
Be sure to show clearly all the calculations it takes to get this.
(c) If you were using alpha =.10, what
would you conclude based on the p-value for the test statistic?
(d) What assumptions did you make to do
this test?
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5. You have data on 11 Western countries.
You are interested in the difference in how much countries spend on old
age benefits vs family benefits. You have the following data from your
sample (in 1980 $s per eligible person):
The correlation between the two variables
is .07.
(a) Construct a 95% confidence interval
for the average difference between old age and family benefits. Be sure
to show the pieces you calculate to do this.
(b) In words, what does this mean?
(c) What assumptions did you make to calculate
this interval estimate?
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| 6. One concern of sociologists is the
effect of family background on social resources. One way this has been
studied is by looking at the effect of parental (usually paternal) socioeonomic
status on the child's education. You do a regression to check this out.
EDUC is years of education the respondent has and PASEI is a measure of
father's socioeconomic status, which can theoretically go from 0 (very
low status occupation) to 100 (highest status occupation). You get the
following Stata output:
. regress educ pasei
Total | 19921.4414 2319 8.590531 ------------------------------------------------------------------------------
(b) How much variation in education is
explained by father's SEI? Is this a little or a lot or what?
(c) What do "Coef." for PASEI and CONS
estimate?
(d) Is the effect of father's SEI on education
statistically significant? At what level, if it is significant?
(e) In words, describe the effect of father's
SEI on respondent's education.
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7. You know that µ=10. You have two estimators of µ: M1, with E{M1}=9
and sigma2 {M1}=10
Which estimator do you prefer and why?
8. The number of students who speak in
class on any given day is a discrete uniform random variable X., with parameters
a=1 and s=11.
(a) What is E{X}?
(b) What is sigma2 {X}?
(c) What is P (2<X<=4)?
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