Home Exercise on Hypothesis Testing and Chi-Squared Test Analysis

This document presents a solution to a graded home exercise focused on hypothesis testing and chi-squared tests. The assignment involves analyzing data related to antidepressant use in a French population, comparing prevalence rates at national and regional levels. The solution includes calculations, statistical tests, and interpretations of results, including the use of contingency tables to assess differences in antidepressant use between genders. The student demonstrates an understanding of null and alternative hypotheses, p-values, and the appropriate application of statistical tests to answer specific research questions about population prevalence and differences between groups.

Graded home exercise - Part I
Assessment part I
Following the first lectures on hypothesis testing and chi-squared test, answer the following
home exercise questions to evaluate your knowledge and understanding.
A nationwide population-based study has reported that the prevalence of antidepressant use is
15% in the French population.
A cross-sectional study was conducted among a random sample of 500 patients attending the
oncology departments of 5 teaching hospitals of the South-Western region in France.
Among them, 150 patients were found as antidepressant users.
Question 1. (5 pts)
In this sample, does the prevalence of antidepressant use differ significantly from the one found
at the national level?
Answer: Null hypothesis: There is no significant difference on prevalence of antidepressant at
the national level.
Alternative hypothesis: There is a significant difference on prevalence of antidepressant at the
national level.

Table 1 T test output
It has been seen that the P-value is larger than the alpha at 5%. Hence the null hypothesis of this
test is accepted. This it may be summarized that there is no significant difference on prevalence of
antidepressant at the national level.
Question 2. (10 pts)
From interviews conducted among the general physicians, it was found that among the 500
patients, 250 patients were women and out of them 100 were antidepressant users.
We want to answer the question:
Is the prevalence of antidepressant use different between women and men in this sample?
Answer: Total number of patients = 500
Number of women patients = 250

The number of women antidepressant users = 100
- What is the type of the two variables studied: gender and antidepressant
- Are the variables categorical, discrete or continuous?
- State the null and alternative hypotheses.
Answer: It is a discrete Categorical variable.
Null hypothesis: There is no difference between women and men on prevalence of
antidepressant
Alternative hypothesis: There is a difference between women and men on prevalence of
antidepressant
Fill in the below 2x2 contingency Tables 1 and 2 below:
Table 1. Observed results of the antidepressant drug use according to gender
Gender/
antidepressant
Yes No total
woman 100 150 250
men 0 250 250
total 100 400 500
Table 2. Expected cell counts if the null hypothesis is true
Gender/
antidepressant
Yes No Total
Woman 50 200 250
Men 50 200 250
Total 100 400 500
Chi-square test statistic = 125
P-value = 0.000
Alpha = 0.05 (at 5%)
It has been seen that the P-value is lesser than the alpha. Hence the null hypothesis of
this test is rejected and the alternative hypothesis is accepted. Thus it may be summarized
that there is a difference between women and men on prevalence of antidepressant.

Question 3. (5 pts)
3a. What is the prevalence of antidepressant use in women and in men?
Answer: There is a difference between women and men on prevalence of antidepressant
3b. Which test is suitable to answer the question about the difference of prevalence in men and
women?
Answer: The chi-square test has been applied to test the difference of prevalence in men and
women.