Homework #3 requires you to complete five questions related to our lectures on “Sampling,
Inference, & Estimation.” Please, show all of your work, type your answers, and
upload a .pdf version of your answers to D2L before the deadline (see, Syllabus).
In addition, you must fully explain the substantive results from your findings. A mathematical
answer is not enough to get credit. You must write a substantive response
as if you were explaining the result in a journal article.
1. What is the Central Limit Theorem (CLM)? Explain the logic of the CLM. How does the CLM
relate to the concepts of population, sample, parameter, statistics, representative, and EPSEM?
(Your answer should be at least one half page, i.e. two paragraphs.)
2. A sample of 101 countries were selected for a study on gender and public policy. In the sample,
the mean number of days paid that a woman could take for maternity leave was 138. The standard
deviation was 32. Calculate a 99% (α = 0.01) confidence interval for the number of paid maternity
days a women receives.
3. The General Social Survey (GSS) commonly has a question that asks American respondents
about the number of sexual partners they have had over their lifetime. Let’s say that in 2016, the
mean number of sexual partners was 8 with a standard deviation of 2.3. The number of participants
in the survey were 231. Calculate a 95% (α = 0.05) confidence interval for number of sexual
partners Americans have had over the lifetime.
4. As Wisconsin is fairly well known for excessive drinking, in 2005 the University of Wisconsin
System conducted a study that surveyed college students in order to investigate alcohol and drug
use. In terms of alcohol use, 15,232 students were surveyed. Of the 15,232 students, 12,186 indicated
that they had used alcohol in the last month. Calculate a 99% (α = 0.01) confidence interval
for the proportion of students that used alcohol.
5. In a subset of the same University of Wisconsin Survey (2005), 21 out of 100 students indicated
that their alcohol consumption led to them engaging in unprotected sex and 45 out of 100 indicated
that they had blackouts in the last year. Calculate a 95% (α = 0.05) confidence interval for the
proportion of students that engaged in unprotected sex in the last year. Then, calculate a 95% (α
= 0.05) confidence interval for the proportion of students that blacked out in the last year.