Does average self-reported weekly income differ between male and female full-time workers in Sydney?

401077 Introduction to Biostatistics, Autumn 2019
Assignment 2
Statistics
Student Name:
Instructor Name:
Course Number:
22 April 2019

Question 1 (12 marks)
Research question: Does average self-reported weekly income differ between male and
female full-time workers in Sydney?
In the following analyses, use R Commander and the assignment data set assigned to you.
The variables you will use are ‘sex’ and ‘income’ and ‘log_income’. Each student will get
different answers as the data sets differ.
a) Using R Commander, graph the distributions of income for males and females
separately. Write a sentence describing the shape of these distributions. Repeat for
the logarithm transformed values of income (variable: log_income). (2 marks)
Answer
The first graph is presents the income histogram for the male and females
separately. As can be seen, the graphs clearly shows that the distribution for the
income for both the male and females is skewed (right-skewed)
The second graph presents the log income histogram for the male and females
separately. As can be seen, the graphs clearly shows that the distribution for the log
income for both the male and females is close to normal distribution.

b) The research question could be addressed by conducting either an independent
samples t-test on the difference in mean ‘income’ between genders or an
independent samples t-test on the difference in mean ‘log_income’ between
genders. Which of these two alternatives would you chose? Justify your choice. (2
marks)
Answer
I would chose an independent samples t-test on the difference in mean ‘log_income’
between genders. This is because one of the conditions for a t-test is that the data
should follow a normal distribution and from a) above, log_income was close to
normal distribution as compared to the income which was heavily skewed.
c) Using R Commander, implement the analysis you chose in b). Present your results
using the 5-step method. (4 marks)
Answer
Step1: Specifying the Hypothesis
We sought to test the following hypothesis
Null hypothesis (H0): There is no significant difference in the mean log_income
between the genders.
Alternative hypothesis (HA): There is significant difference in the mean log_income
between the genders.
Step 2: Set the Significance Level (a)
5% level of significance will be used to make a decision on whether to reject or to
accept the null hypothesis.
Step 3: Making a decision
Null hypothesis will be rejected if the computed p-value is less than the significance
level (α = 0.05)
Step 4: Computing the test statistic and the corresponding p-value
An independent samples t-test was used to test the hypothesis. The results of the
test are given in the table below;
The results of the independent t-test are
shown above, the p-value is given as 0.8819
(a value greater than 5% level of
significance), we therefore fail to reject the
null hypothesis
Step 5: Drawing conclusion
Since the null hypothesis was not rejected,
we conclude that there is no significant
difference in the mean log_income between
the genders.
> t.test(log_income~sex)
Welch Two
Sample t-test
data: log_income by sex
t = -0.1487, df =
452.903, p-value =
0.8819
alternative hypothesis:
true difference in means
is not equal to 0
95 percent confidence
interval:
-0.1269623 0.1091013
sample estimates:
mean in group male
mean in group female
7.31741
7.32634