STAT 130
Fall 2018
Case Study
Wentworth Medical Center
As part of a long-term study of individuals 65 years of age or older, sociologists
and physicians at the Wentworth Medical Center in upstate New York
investigated the relationship between geographic location, gender and depression.
A sample of 60 individuals, all in reasonably good health, was selected; 20
individuals were residents of Florida, 20 were residents of New York, and 20
were residents of North Carolina. Each of the individuals sampled was given a
standardized test to measure depression. The data collected follow; higher test
scores indicate higher levels of depression.
You should consider the following instructions when answering the case
study questions and preparing your report:
I.
For confidence intervals:
➢ Check all assumptions.
➢ Interpret the results.
II.
➢
➢
➢
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III.
For testing hypothesis:
State the null and alternative hypotheses.
Check the necessary assumptions.
Report the P-value and the test statistic.
Make a conclusion statement in the words of the original problem.
For the report
➢
➢
➢
➢
➢
Should be typed.
On the first page, write the names, student numbers, and section number.
All pages must be stapled together.
Show all of your work.
The report should have the following item:
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Title
Table of Contents
Executive Summary
Introduction
Main text
Conclusions
Recommendations
STAT 130
Fall 2018
Case Study
Case Study Questions: answer all the following questions and write your
report.
a) Use descriptive statistics to summarize the data.
b) Develop a 95% confidence interval estimate of the mean depression value
for the 60 individuals.
c) Develop a 95% confidence interval estimate of the mean depression value
for residents of Florida.
d) Is the mean of depression value for the 60 individuals different than 5.5?
Use a 0.05 level of significance (test the hypotheses using both p-value
and C.I method).
e) Is there any significant difference of the mean of depression value due to
gender? Use a 0.05 level of significance.
f) Develop a 95% confidence interval estimate of the mean of depression
value difference for male and female.
g) Explain how your conclusion in part e can be derived from part f.
h) Is there any significant difference of the mean of depression value due to
geographic location? Use a 0.05 level of significance.
i) Give point estimates for the proportion of individuals according to their
gender.
j) Is there a difference in the proportions of female between New York and
North Carolina states? Use a 0.05 level of significance.
k) Develop a 95% confidence interval of the difference in proportion of
male between New York and North Carolina states.
STAT 130
Fall 2018
Case Study
l) Is the depression in gender affect by the Geographic locations? Use a
0.05 level of significance.
m)
locations
Number of depressed
persons
Florida New York North Carolina
23
17
20
Is the distribution of the depressed peoples across locations uniform
(𝑃𝐹𝐿 = 33%, 𝑃𝑁𝑌 = 33%, 𝑃𝑁𝐶 = 33% )? Use a 0.05 level of significance.