Gov. 50/Govt E 1005, Prof Spirling
Students of the College must turn in to Professor Spirling’s mailbox by4pm on Thursday Nov
13th(no later!). Students of the Extension School should follow the dropbox instructions on the
class website. Note that the course academic honesty policy applies to every homework, including
this one. Take note that this homework uses the Bostonvoters2014.sav and subprime.sav datasets
located on the course website.
Homework 4
1. Answer true or false to the following. If `false’ explain why and/or give a counter-example.
(a) The sampling distribution of sample means is centered at xwith a variance of
2
n
.
(b) The bin that represents the modal category of a histogram always contains the mode of
the data.
(c) If the population distribution has a right skew, the mean of the sampling distribution of
sample means will typically be greater than the median of the sampling distribution.
(d) The sample mean can be less than the lower quartile.
(e) The standard deviation of the sampling distribution, the standard error, gets closer to
the population standard deviation as sample size increases.
(f) A sample for which the 25th percentile is equal to the 75th percentile is composed of
identical values only.
2. Read the attached article \How Much Film Violence for Kids?” before answer the questions
below (if you are interested in the original study, it is called \Gun Violence Trends in Movies,”
and was published in the December 2013 issue of the journalPediatrics).
(a) What is the sample size for the study in the story?
(b) Suppose the standard deviation of acceptable ages for watching violent movies is 2.2
years. What is the variance?
(c) The mean age that parents believed to be acceptable for watching violent movies after
viewing all six clips is 13.9. Assume that the standard deviation is 2.2, as above. Assum-ing that the ages at which parents believe it is acceptable to watch violent movies are
normally distributed, calculate the percentage of parents who believe that these movies
are acceptable for children who are less than 12 years old.
(d) Calculate the percentage of acceptable ages greater than 17 after the last clip.
(e) After the last clip what proportion of acceptable ages are between 14 and 12 years?
1
(f) Suppose the researchers decide to re-run the experiment with a new sample of parents,
this time including a control group. They randomly assign half of the parents to watch
a sequence of violent movie clips (\treatment”), and half of the parents to watch a se-quence of non-violent cartoons (\control”). After watching their assigned clips, parents
in both groups are asked to state the age at which children should be permitted to watch
violent movies. Compared to those in the treatment group, parents in the control group
report much higher ages on average. Sketch the new distribution of ages reported by all
of the parents (no need to get the scale correct), showing the rough position of the new
mean and median.
(g) Suppose a researcher at a particular university has not read the report (and thus does
not know the mean), but has been informed of the standard deviation for the population
of acceptable ages stated by parents who have been exposed to the scenes depicting
violence (as stated in part b). She re-runs the experiment with 36 parents and observes
that x= 12:5. Construct an 80% con dence interval for this mean.
(h) A researcher at a very small university does not have access to the report, its mean,
or variance. She does, however, have a small sample of ve parents. After running an
identical study to the one rst described in the article, she observes that the acceptable
ages to watch violent movies are 17, 10, 7, 13, 15 years old, respectively. What is the
mean age after exposure to violent movies?
(i) What is the standard deviation?
(j) What is the median?
(k) Are there any outliers? Brie
y explain.
(l) Calculate a 98% con dence interval around x.
(m) The chair of the department at the small university asks the research to summarize her
ndings. The researcher says that there is a 98% chance the mean acceptable age is in
the interval she calculated. Is this inference correct? If not, give the correct interpreta-tion.
3. In this problem, you will use a dataset called subprime.sav, which contains a sample of
applicants for a loan. The income, gender, and race of applicants are indicated by income,
woman, and black, respectively. The variable black has a value of 1 when the applicant
identi es as African-American and 0 otherwise. The variable high.rateindicates whether the
applicant received a subprime loan, a loan o ered at high interest rates for people who may
have diculty repaying the loan. The variablehigh.ratehas a value of 1 when the applicant
received a subprime loan and 0 otherwise.
2
(a) Using a maximum of three intervening steps, write a sensible causal story that might
link the variables of race, black, and receiving a high rate loan, high.rate.
(b) Using the boilerplate from lecture, write a hypothesis that asserts a sensible relationship
between the variables of race and receiving a high rate loan.
(c) What is the null hypothesis here?
(d) Using SPSS, present a cross-tab with appropriate percentages.
(e) Without doing an explicit hypothesis test, comment on whether or not the table sup-ports your hypothesis.
(f) Conduct a hypothesis test. Report the chi-squared test statistic and the relevant p-value.
(g) Is the nding statistically signi cant? At what level?
(h) Use SPSS to calculate lambda for this association. What is its value? Why?
(i) Consider an alternative measure and present the results.
(j) How strong is the relationship betweenblackandhigh.rate?
4. In this problem you will use a dataset from your previous homework, Bostonvoters2014.sav,
which contains a sample of Boston homeowners who are currently registered to vote in Boston.
Recall that the voter’s occupation, age, gender and party registration are indicated byOccpt,
Age, Gender, and Party, respectively. The variables Voted2012andVoted2013are indicators
for whether the individual voted in 2012 and 2013, respectively. The 2013 assessed home
value in U.S. dollars isHomevalue, the home value divided by the number of square feet of
living space in the home is Valuepersqft, and the neighborhood in which the home is located
is Neighborhood.
(a) In SPSS, create a scatterplot with voter age on the horizontal axis and home value on
the vertical axis. Comment on the relationship between home value and voter age. Does
home value appear to have \greater spread” or variation at certain voter ages? Be sure
to include a copy of your scatterplot in your answer.
(b) Based on the scatterplot, roughly how old is the voter with the most valuable home in
the dataset?
(c) Using the \Compare Means” function in SPSS, create a table that lists the average
home value for voters in each neighborhood. What neighborhood is associated with the
highest average home value? What neighborhood is associated with the lowest average
home value? What is the modal neighborhood in the sample? Be sure to include a copy
of your table in your answer.
3
(d) The researcher wants to know if Democrats and Republicans are, on average, statistically
di erentiable in terms of age. What kind of hypothesis test should she run to assess
whether Democrats and Republicans are equal in age? In your answer, explicitly state
the null and alternative hypotheses (either in words or using correct notation). You
should treat the age variable as interval and ignore \undeclared” voters for now.
(e) In SPSS, implement the hypothesis test from part (c), and state the p-value associated
with this test. Give the degrees of freedom used in this case (assuming \equal variances”).
Does there appear to be a statistically signi cant relationship at the 95% level?
4
Figure 1: News article excerpt for Question (2).
The Christian Science Monitor
How much film violence for kids? Parents losing their compass, study says.
A new study shows that the more parents watch violence and sex in TV shows and
movies, the more permissive they are of what their kids can watch. The results were
‘stunning,’ one researcher said.
By Stephanie Hanes, Correspondent, OCTOBER 20, 2014
Parents who watch multiple movie scenes of sex and violence quickly become more
permissive about how old a child should be to watch films with disturbing content,
according to a study released today in the journal Pediatrics.
Researchers from the Annenberg Public Policy Center at the University of Pennsylvania
showed a nationally representative sample of 12,000 parents six different film clips from
movies rated R and PG-13, such as “Terminator,” “8 Mile” and “Taken 2.” After each
scene, which either showed violent or sexual conduct, they asked the parents at what age
a child should be before watching the movie.
Regardless of the order in which they viewed the scenes, the parents started off relatively
conservatively, saying on average that a child should be about 17 years old before he or
she watched the movie in question. With each succeeding clip, though, the parents
reduced this age judgment. By the last clip, parents set an average age of 13.9 for
watching the violent movies and 14 years for the movies that included the sex scenes.
5
PLACE THIS ORDER OR A SIMILAR ORDER WITH US TODAY AND GET AN AMAZING DISCOUNT 🙂