Introduction to Bio-Statistics

Introduction to Bio-Statistics
Student Name:
Instructor Name:
Course Number:
6th May 2019
Question 1 (12 marks)

a) Graphing the distributions;
Answer
Figure 1: Histogram for male and female income levels
In figure 1 we have the histograms for the male and female income levels.
We can see that the two histograms (both for the male and female income
levels) are heavily skewed to the right (longer tails to the right).
Figure 2: Histogram for male and female income levels
In figure 2 we have the histograms for the male and female log-income
levels. We can see that the two histograms (both for the male and female
income levels) unlike the first ones seem to follow a normal distribution
(bell-shaped curve).
b) Choice of the two alternatives
Answer

I would go for the log-incomes levels. This is because the above
figures shows that the log-income levels follow a normal distribution
which is a key assumption for a t-test.
c) Presenting the results
Answer
Step 1: Stating the null hypothesis
H0 : μm=μf
H A : μm ≠ μf
Where μm =the averagelogincome for the males
μf =the average logincome for the fe males
Step 2: Stating the test statistic and the significance level
For this hypothesis, an independent t-test will be performed at 5%
level of significance (α = 0.05).
Step 3: Stating the decision rule
Null hypothesis will be rejected if the computed p-value is less than
the level of significance (α = 0.05).
Step 4: Computing the test statistic
In this section, we present the results of the computed test statistic
from R.
Step 5: Making a conclusion
From the above results, we can see that
the p-value is 0.9016. This value is much
greater than the level of significance (α
= 0.05). We therefore fail to reject the
null hypothesis and conclude that the
average log-income for the male and the
females is not different at 5% level of
significance.
d) Presenting the results of a non-
parametric test
Answer
Step 1: Stating the null hypothesis
H0 : Randomly selected value of the loginocme is same for male∧females
H A : Randomly selected value of theloginocme is different for male∧females
Step 2: Stating the test statistic and the significance level
For this hypothesis, a Mann-Whitney U test will be performed at 5%
level of significance (α = 0.05).
Step 3: Stating the decision rule
> t.test(log_income~sex)
Welch Two
Sample t-test
data: log_income by sex
t = -0.1237, df =
488.261, p-value =
0.9016
alternative hypothesis:
true difference in means
is not equal to 0
95 percent confidence
interval:
-0.1324269 0.1167365
sample estimates:
mean in group male
mean in group female
7.242235
7.250081