1. Case study Presentation by:
Obakeng Gabasie
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2. Title: To analyze and compare the
performance of Mathematics and
Applied Statistics for Year 1 & 2 at
EASTC in 2011.
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3. Aim of the Case Study
To compare two subjects: Mathematics and Applied Statistics
data sets for year 1 and 2 for the performance of students
Objectives
 To compare the performance of students in Mathematics and
Applied Statistics for year 1 and 2
 To show the difference between the mean of two subjects:
Mathematics and Applied Statistics for year 1 and year 2
 To examine that the two subjects: Mathematics and Applied
Statistics are independent or dependent.
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4. Methodology
 Secondary data of six subjects was given of which we were
required to choose two subject to compare.
 Analyzing data by using SPSS and Microsoft Office Excel
2007.
 I used multiple bar charts to compare the performance of
student
 I also used the Z – test to the difference in mean of
Mathematics and Applied Statistics
 And chi-square (ᵡ2) to examine that the two subjects:
Mathematics and Applied Statistics
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5. Some Statistical Hypothesis abbreviations and
definitions
 H0: Null Hypothesis
 H1: Alternative Hypothesis
 α: Level of significance
 ᵡ2: Chi-Square
 Z: Z-test
Null Hypothesis (H0)
 specifies a particular value for some population parameter.
Alternative Hypothesis (H1)
 Specifies a range of values.
Level of significance (α):
The probability of claiming a relationship between
independent and dependent variable.
Chi – Square (ᵡ2)
 Is a statistical method used to test whether the variable are
dependent or independent.5

6. For chi-squared I only considered the
following table
When calculating the chi-square from the statistical table I use the
following formula
α (R-1)(C-1)
Whereby:
R is the number of rows
C is the number of columns
Grading Remarks
0-49 Fail
50-100 Pass
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7. Tools used
 SPSS for analyses of the data
 Microsoft excel 2007 for designing the work plan and analysis
of the data
 Microsoft word for typing the final report
 Printer for printing the hardcopy document
 Microsoft power point 2007 for presenting my individual case
study
The procedure to calculate the chi-square and Z-test.
Write down H0 and H1
Determine the acceptance and rejection region
Calculate the value of the test
Decision and conclusion based on the H0 and H1.
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8. Assumptions
 The data sets of Mathematics and Applied Statistics are based
on the assumption that data are sample mean and normally
distributed meaning that the data comes from the same
population with a mean and variance of 0 and 1.
 And also the following assumption were made in the grading
tables.
Grading Remarks
75 - 100 Distinction
65 - 74 Credit
50 - 64 Pass
0 - 49 Fail
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9. FINDINGS
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10. Comparing the performance for
mathematics year 1 and 2
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11. Figure 1: Multiple bar chart of Mathematics for year 1
and 2
From the above figure we can see that there were only 14% of
students who failed in year 2 while in year 1 there were only
8%. Also there were 24% students who got distinction in year
2 while for year 1 there were only 30%.
30%
20%
42%
8%
24%
24%
38%
14%
Distinction
Credit
Pass
Fail
Performance
Year2
Year1
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12. Table 2: shows the paired samples statistics of Mathematics for
year 1 and year 2
 Formulation Of Null Hypothesis
Ho : µ1= µ2
H1 : µ1>µ2
 The level of Significant
α = 0.05 (5%)
 Formulation of Decision
To reject Ho if Z(1.012) is greater than Zα (in statistical
table).
Mean N
Std.
Deviation z
Subjects
Maths1 67.11 69 15.576 1.012
Maths2 62.43 37 19.558
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13.  Testing Statistics
Zα = Z0.05 = 1.645
Z (1.012) < 1.645
 Decision
Do not reject Ho
 Conclusion
We conclude that the student’s mean performance for year 1
in mathematics is greater than the mean performance of
mathematics in year 2.
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14. Table 3: shows the cross tabulation of the performance
of Mathematics for year 1 and 2
 Formulation of Null Hypothesis
Ho: There is no association between performance and the
level studies of (year one and year 2).
H1: There is association.
 Level of Significant
α = 0.05 (5%)
Mathematics
Total
Chi-square
Year1 Year2
Performance Pass
65 32 97
1.846
Fail
4 5 9
Total
69 37 106
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15.  Formulation Of Decision
To reject Ho if (1.846) is greater than α (R-1)(C-1) (from statistical
table)
 Testing Statistics
0.05,1 = 3.841
(1.846) < 3.841
 Decision:
Do not reject Ho
 Conclusion
There is no enough evidence to associate difference between
performance of students in mathematics for year 1and 2 and the level of
studies.
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16. Comparing the performance of
Applied Statistics for year 1 and
year 2
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17. Figure 3: Multiple bar chart of Applied Statistics
3%
28%
48%
22%
16%
14%
62%
8%
Distinction
Credit
Pass
Fail
Performance
Year2
Year1
From the multiple bar charts (in percentages) it shows that 3% and 16% obtained
distinction and 22% and 8% failed in year 1 and 2. And also 76% passed in year 1
and 2 respectively.
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18. Table 4 shows the paired samples statistics of Applied
Statistics for year 1 and year 2
Subjects
Mean N Std.
Deviation Z
Applied
Statistics
Year 1
54.41 69 10.743
-2.398
Applied
Statistics
Year 2
60.59 37 12.840
 Formulation Of Null Hypothesis
Ho : µ1= µ2
H1 : µ1<µ2
 The level of Significant
α = 0.05
 Formulation Of Decision
To reject Ho if Z(-2.398) is less than Zα (from statistical table)
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19. Testing Statistics
Zα = Z0.05 = -1.645
Z (-2.398) < -1.645
Decision
Do not reject Ho
Conclusion
We conclude that the student’s mean performance for year 2 in
Applied Statistics is less than the mean performance of Applied
Statistics in year 2.
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20. Table 5: Cross tabulation showing the performance of Applied Statistics
for year 1 and 2
 Formulation of Null Hypothesis
Ho: There is no association between performance and the level of studies (year 1
and year 2).
H1: There is association.
 Level Of Significant
α = 0.05 (5%)
 Formulation Of Decision
Reject Ho if (1.955) is greater than α (R-1)(C-1) (in statistical table)
Cross tabulation
Level
Total
Chi -
SquareYear 1 Year 2
Performanc
e
Pass 54 33 87
1.955
Fail
15 4 19
Total 69 37 106
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21.  Testing Statistics
0.05,1 = 3.841
(1.955) < 3.841
 Decision:
Do not reject Ho
 Conclusion
There is no enough evidence to associate difference between
performance of students in Applied Statistics for year 1and 2 and
the level of studies.
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22. Conclusion
When comparing the two subjects I found that 8% and 14% of students failed
and 30% and 24% students obtained distinction in Mathematics in year 1 and
2, while in Applied Statistics 3% and 16% of students obtained distinction, and
22% and 8% of students failed in year 1 and 2.
The performance of students in year 1 is better than the student of year 2 in
Mathematics, while for Applied Statistics the student in year 2 performed
better than year 1.
At the 5% level of study, from the sampled data, there is no sufficient
evidence to conclude that Mathematics and Applied Statistics are associated.
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23. THANK YOU!!!!
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