Calculating t-tests for Independent and Paired Samples - Exercise 31 and 32

RUNNING HEADER: STATISTICS 1
Name Course HLT362v
Date Section
EXERCISE 31
Calculating t-tests for Independent Samples
1. Do the example data meet the assumptions for the independent samples t-test? Provide
a rationale for your answer.
The given data meets all the assumptions for an independent samples t-test. The validation for
this is that:
 Independent observations: Each case represents a different statistical unit (Controlled and
supported employment).
 Normality: The dependent variable follows a normal distribution in the population. The
test for normality is as shown in the table below:
Table 1: Normality Test
Kolmogorov-Smirnov Shapiro-Wilk
Statistic df Sig. Statistic df Sig.
Wages Received Per Week 0.155 20 0.200* 0.935 20 0.194
Only the test of the Shapiro-Wilk is focused on since the cases are less than 2000. Since P >
0.05, the null hypothesis is cannot be rejected and it can be established that the data is derived
from a normal distribution.

Statistics 2
 Homogeneity: since the sample sizes are equal, there was no need to conduct the
homogeneity test. The assumption is only tested when the sample sizes are (sharply)
unequal (Mayers, 2013).
2. If calculating by hand, draw the frequency distributions of the dependent variable,
wages earned. What is the shape of the distribution?
Figure 1: Frequency distribution
From figure 1, it is evident that the shape of the distribution is bell-shaped, thus the variable
follows a normal distribution.
If using SPSS, what is the result of the Shapiro-Wilk test of normality for the dependent
variable?
From table 1, the outcome of the test of normality for Shapiro-Wilk was a statistics of 0.935 with
a p-value of 0.194. Hence the conclusion that the data is derived from a normal distribution since
the p-value is greater than 0.05.
3. What are the means for two group’s wages earned?
Table 2: Groups descriptive statistics
Treatment Group N Mean Std. Deviation Std. Error
Mean
Wages Received Per Week Control 10 $128.40 $43.025 $13.606
Supported Employment 10 $232.70 $65.325 $20.658

Statistics 3
The means of the wages received per week of the control group is $128.40 ± $43.03 while the
mean of the wages received per week of the supported employment is $232.70 ± $65.33.
4. What is the independent samples t-test value?
Table 3: Independent Samples Test
Levene's Test for
Equality of
Variances
t-test for Equality of Means
F Sig. t df Sig. (2-
tailed)
Mean
Difference
Std.
Error
Differenc
e
95% Confidence
Interval of the
Difference
Lower Upper
Wages
Received
Per
Week
Equal
variances
assumed
2.477 0.133 -4.217 18 0.001 ($104.30) $24.74 ($156.27) ($52.33)
Equal
variances
not
assumed
-4.217 15.572 0.001 ($104.30) $24.74 ($156.86) ($51.75)
From the Levene’s test, since the significance is greater than 0.05. Thus, the tests of equal
variances assumed holds. Therefore, the independent sample t-test value is -4.217.
5. Is the t-test significant at a = 0.05? Specify how you arrived at your answer.
From the test on equal variances assumed it is seen that the significance is less than 0.05. Thus,
we choose to not accept the null hypothesis since the t-test is significant statistically and
conclude that the population means are not equal.
6. If using SPSS, what is the exact likelihood of obtaining a t-test value at least as extreme
or as close to the one that was actually observed, assuming that the null hypothesis is
true?
From table 3 above, it is evident that the precise probability of obtaining a t-test value which is
either as extreme or as close to the one that was really perceived with the assumption that the
null hypothesis is true is 0.1%.