INFERENTIAL STATISTICS: CASE OF SUN COAST COMPANY
26
The scale of measure for all the data variables are ratio. This is because all the difference in value
is significant as well as the ratio.
T-test for two comparing training results
The hypothesis for this test is;
H0: µ1 = µ2
Ha: µ1 ≠ µ2
t-Test: Two-Sample Assuming Unequal Variances
Group A Prior Training Scores
Group B Revised Training Scores
Mean
69.79032258
84.77419355
Variance
122.004495
26.96456901
Observations
62
62
Hypothesized Mean Difference
0
Df
87
t Stat
-9.666557191
P(T<=t) one-tail
9.69914E-16
t Critical one-tail
1.662557349
P(T<=t) two-tail
1.93983E-15
t Critical two-tail
1.987608282
T-test for difference in mean
The average result for training A is 69.79, while that for B is 84.77, the critical value for
two-tailed, 1.9876 is greater than the p-value for two-tailed = 1.93983E-15, this implies that
there is significant difference in mean for the two samples. The p-value is also smaller than the
level of significance α = 0.05, thus we reject H0 and conclude that the population mean for the
training outcomes is significantly different. The revised training is superior.
The two samples were drawn from normally distributed populations as indicated by the
shapes of the histograms. The sample size is also large enough to be used for test since there are
62 pairs of observations. The scale of measurement for the data is ratio since they are training
results. The data were drawn using random sampling technique as the run tests indicate
randomness. Thus the test is valid since the assumptions are met (Xue, & Titterington, 2011).
INFERENTIAL STATISTICS: CASE OF SUN COAST COMPANY
27
Group A Prior Training Scores
50
55
60
65
70
75
80
85
90
95
Frequency
4
5
3
11
9
10
11
3
5
1
Frequency Distributions for Group A training results
Group B Revised
74
76
78
80
82
84
86
88
90
92
94
96
98
Frequency
0
4
3
7
6
9
11
7
7
4
1
2
1
Frequency Distributions for Group B training results
0
5
10
15
Group A
Frequency
Group B Revised Training Scores
Frequency
0
5
10
15
Group B
Frequency
Group A Prior Training Scores
Frequency
Histogram representation for both variables
Group A Prior Training
Group B Revised Training
Mean
69.79032258
Mean
84.77419355
Standard Error
1.402788093
Standard Error
0.659478888
Median
70
Median
85
Mode
80
Mode
85
Standard Deviation
11.04556449
Standard Deviation
5.192741955
Sample Variance
122.004495
Sample Variance
26.96456901
Kurtosis
-0.77667598
Kurtosis
-
Skewness
-
Skewness
0.144084526
INFERENTIAL STATISTICS: CASE OF SUN COAST COMPANY
28
Range
41
Range
22
Minimum
50
Minimum
75
Maximum
91
Maximum
97
Sum
4327
Sum
5256
Count
62
Count
62
Confidence Level (95.0%)
2.805048156
Confidence Level (95.0%)
1.318709538
Descriptive statistics for the variables
Measures of central Tendency
The mean mode and media for both variables indicate a slight variations and thus
indicating that the population from which the data was draw follow a normal distribution. This
can also be observed from the shapes of the histograms. The histograms are bell shaped.
