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Case study Presentation by:
Obakeng Gabasie
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Title: To analyze and compare the performance of Mathematics and Applied Statistics for Year 1 & 2 at EASTC in 2011.
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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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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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Some Statistical Hypothesis abbreviations and definitions
H0: Null Hypothesis H1: Alternative Hypothesis α: Level of significance ᵡ2: Chi-Square Z: Z-testNull 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
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 Remarks0-49 Fail50-100 Pass
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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 regionCalculate the value of the testDecision and conclusion based on the H0 and H1.
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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 Remarks75 - 100 Distinction65 - 74 Credit50 - 64 Pass0 - 49 Fail
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FINDINGS9
Comparing the performance for mathematics year 1 and 2
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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%.
Distinction
Credit
Pass
Fail
30%
20%
42%
8%
24%
24%
38%
14%
Year2Year1
Performan
ce
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Table 2: shows the paired samples statistics of Mathematics for year 1 and year 2
Formulation Of Null HypothesisHo : µ1= µ2 H1 : µ1>µ2 The level of Significantα = 0.05 (5%)Formulation of DecisionTo 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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Testing StatisticsZα = Z0.05 = 1.645Z (1.012) < 1.645
DecisionDo 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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Table 3: shows the cross tabulation of the performance of Mathematics for year 1 and 2
Formulation of Null HypothesisHo: There is no association between performance and the
level studies of (year one and year 2).H1: There is association. Level of Significantα = 0.05 (5%)
Mathematics
Total
Chi-square
Year1 Year2Performance
Pass 65 32 971.846Fail 4 5 9
Total 69 37 106
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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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Comparing the performance of Applied Statistics for year 1
and year 2
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Figure 3: Multiple bar chart of Applied Statistics
Distinction
Credit
Pass
Fail
3%
28%
48%
22%
16%
14%
62%
8%
Year2Year1
Perf
orm
ance
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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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 260.59 37 12.840
Formulation Of Null HypothesisHo : µ1= µ2 H1 : µ1<µ2 The level of Significantα = 0.05Formulation Of DecisionTo reject Ho if Z(-2.398) is less than Zα (from statistical table)
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Testing Statistics Zα = Z0.05 = -1.645Z (-2.398) < -1.645
DecisionDo 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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Table 5: Cross tabulation showing the performance of Applied Statistics for year 1 and 2
Formulation of Null HypothesisHo: There is no association between performance and the level of studies (year 1 and year 2).H1: There is association. Level Of Significantα = 0.05 (5%) Formulation Of DecisionReject Ho if (1.955) is greater than α (R-1)(C-1) (in statistical table)
Cross tabulationLevel
TotalChi - SquareYear 1 Year 2
Performance
Pass 54 33 871.955Fail 15 4 19
Total 69 37 106
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Testing Statistics 0.05,1 = 3.841 (1.955) < 3.841
Decision:Do not reject Ho ConclusionThere 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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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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THANK YOU!!!!
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