Hypothesis Testing Assignment

Hypothesis Testing
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23rd March 2020

1. Analysis techniques such as t-test or one-way ANOVA assume that the data being compared
comes from normal distributions. Assess the normality of the wage variable in the Wage data set.
Is a normal assumption appropriate? If not, what normal transformation can be applied? In the
comparisons to assess significant differences, you should use the transformed values.
Answer
We assess the normality of the wage variable in the Wage data set using a histogram as shown
below;
From the above histogram, it is evident that the wage variable is not normally distributed but is
rather skewed to the right (longer tail to the right).
We confirm this using Shapiro-Wilk test where the results are presented below;
> shapiro.test(Wage$wage)
Shapiro-Wilk normality test
data: Wage$wage
W = 0.87957, p-value < 2.2e-16
The above results further confirm that the variable wage is does not follow a normal distribution
(p < 0.05).
2. Use an independent t-test to determine whether or not there is a significant difference in wages
for the information and industrial sectors using the variable jobclass.
Answer

Null and alternative hypotheses
In this section we sought to test the following hypothesis;
Null hypothesis (H0): There is no significant difference in the wages for the information and
industrial sectors.
Alternative hypothesis (HA): There is significant difference in the wages for the information and
industrial sectors.
Significance level alpha and corresponding critical t-value
The significance level used is 5% level (α = 0.05) and the corresponding critical t-value is given
as 1.961.
Calculated t-value and corresponding p-value
An independent t-test was computed and the results are presented below;
> t.test(logwage~jobclass)
Welch Two Sample t-test
data: logwage by jobclass
t = -11.468, df = 2948.3, p-value < 2.2e-16
alternative hypothesis: true difference in means is not equal to 0
95 percent confidence interval:
-0.1692574 -0.1198298
sample estimates:
mean in group 1. Industrial mean in group 2. Information
4.583753 4.728297
From the t-test results, the calculated t-value is t = -11.468 and the corresponding p-value is
0.000 (Fay & Proschan, 2014).
Hypothesis test decisions
We reject the null hypothesis if the p-value is less than 5% level of significance and from the
results we will have to reject the null hypothesis (p < 0.05).
Statement as to whether that alternative hypothesis is true
Rejecting the null hypothesis implies that the alternative hypothesis is true.
Description of what the hypothesis means