Practice Problems
1. In the general population, the prevalence of Posttraumatic Stress Disorder (PTSD) is estimated
to be about 5% in male adults. In a southwestern city, 95 male firefighters were randomly
selected and surveyed, and it was found that 10 of the 95 (10.5%) had PTSD.
Research Question - Does this provide evidence that the prevalence of PTSD is higher for
male firefighters in this southwestern city than for males in the general population?
a. Define the population of interest.
All male firefighters
b. Define the sample for the study.
95 firefighters selected
c. Define the variable of interest for the study.
PTSD Status
d. Suppose you wanted to conduct a simulation study to answer the research question of
interest. Using the online applet, carry out a simulation with 500 trials and sketch your
plot below.
You’re graphs will vary, but you should have changed the probability to 0.05
and set the number of tosses to 95 as shown below.
e. Using the plot created in part d, calculate the estimated probability of observing results
at least as extreme as observed.
Using your plot you’ll want to find P(X ≥ 10) =
# dots 10 & above
500
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f.
Using the estimated p-value found in part e, does this study provide evidence that the
prevalence of PTSD is higher for male firefighters in this southwestern city than for
males in the general population? Explain.

If your p-value < 0.05 then there IS EVIDENCE the prevalence of PTSD is
higher for firefighters than for the general population.

If your p-value is > 0.05 then there is NO EVIDENCE the prevalence of PTSD
is higher for firefighters than for the general population.
2. Wagenknect et al. (2002) collected data on a sample of 301 Hispanic women living in San
Antonio, TX. One variable of interest was the percentage of subjects with impaired fasting
glucose (IFG). IFG refers to a metabolic stage intermediate between normal glucose
homeostasis and diabetes. In the study 24 women were classified in the IFG stage. The article
sites population estimates for IFG among women in Texas was 6.3%.
Research Question – Is there sufficient evidence to indicate that the population of
Hispanic women in San Antonio has a prevalence of IFG higher than 6.3%?
a. Define the population of interest.
All Hispanic women living in San Antonio, TX
b. Define the variable of interest for the study.
IFG Status
c. Describe in context how this study can be modeled using a binomial distribution.
1.
2.
3.
4.
n = 301 women
2 outcomes – Have IFG, Does not have IFG
P(IFG) = 0.063 for each Hispanic woman
Hispanic women are independent of each other
d. Assuming 6.3% of women in Texas are classified as having IFG, how many of the 301
Hispanic women living in the San Antonio area would you expect to be classified as
having IFG?
301(0.063) = 18.96
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e. Using JMP, find the probability of observing results at least as extreme as observed.
P(X ≥ 24) = 0.1416
f.
Using the p-value found in part e, does this study provide evidence that the population
of Hispanic women in San Antonio has a prevalence of IFG higher than 6.3%? Explain.
No Evidence (p-value = 0.1416) that the population of Hispanic women living
in San Antonio, TX has a prevalence of IFG higher than 6.3%.
3. A Pew Research Center survey found that 1,120 of the 1,931 adult internet users interviewed
said that the internet has helped them in some way with obtaining health information.
a. Using JMP construct a 95% confidence interval for the true proportion of adult internet
users who say the internet has helped them in some way with obtaining health
information.
b. Interpret the interval found in part a.
95% confident the true proportion of adult internet users who say the internet
has helped them in some way with obtaining health information is between
0.06 and 0.60.
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4. University of New Mexico professor Jane hood investigated the fieldwork methods used by
qualitative sociologists (Teaching Sociology, July 2006). Searching for all published journal
articles, dissertations, and conference proceedings over the previous seven years in the
Sociological Abstracts database, she discovered fieldwork could be categorized as the following:
Interview, Observation + Participation, Observation Only, and Grounded Theory. Furthermore,
it has been hypothesized that 70% of fieldwork conducted is done by interview, 15% using
Observation + Participation, 10% using Observation Only, and 5% using Grounded Theory. The
table below summarizes the number of paper published in the last seven years that fall into
each of the above categories.
Fieldwork Method
Interview
Observation + Participation
Observation Only
Grounded Theory
Total
Number of Papers
5,079
1,042
848
537
7,506
a. Set up the null and alternative hypotheses that would be used to determine if the
observed data are consistent with the hypothesized values.
H0: pinterview = 0.70 pobs + part = 0.15
Ha: Two or more differ
pobservation = 0.10
pgrounded = 0.05
b. Calculate the expected counts that would be used in the computation of the Chi-square
test statistic.
Interview  7506(0.70) = 5254.20
Observation + Participation 7506(0.15) = 1125.9
Observation Only  7506(0.10) = 750.6
Grounded Theory  7506(0.05) = 375.3
c. Using JMP, find the Chi-square test statistic and p-value for this study.
Test Statistic = 94.4023
p-value = 0.0001
d. Using the p-value from part c, is there evidence that the observed data are consistent
with the hypothesized values? Explain.
Evidence (p-value = 0.0001) that the observed data is not consistent with the
hypothesized values.
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