This case study compares student performance in Mathematics and Applied Statistics for Years 1 and 2 at a university. The study aims to compare the mean scores and examine if the subjects are independent. Bar charts show Mathematics failure rates were higher for Year 2 while distinction rates were lower. Applied Statistics saw higher distinction and lower failure rates for Year 2. Hypothesis tests found no significant difference in mean scores for Mathematics but Year 2 performed better in Applied Statistics. Independence tests also found no association between performance and year level for both subjects. In conclusion, Year 2 saw improved Applied Statistics results but worse Mathematics performance compared to Year 1.
This lecture is based on post-graduate medical students of all subject those who are students MS/MD/FCPS of different subject on Central Tendency and Dispersion.
This lecture is based on post-graduate medical students of all subject those who are students MS/MD/FCPS of different subject on Central Tendency and Dispersion.
Name_______________1. A school teacher believes that.docxMARRY7
Name_______________
1.
A school teacher believes that her kindergarten students have higher IQ than average children of that age. She decided to test her hypothesis. The IQ for her class (N=30) was 106, while the population mean () is 100. The standard deviation for her class was 10.
1.1.
State the null and research hypothesis ( & ) (1 POINT)
1.2. Write the statistical conclusion, assuming alpha = .05 (Show your calculations). (1 POINT)
1.3.
Based on your decision to reject or fail to reject , what type of error can you be making? (Choose one) (1 POINT)
Type I error
Type II error
2. A high school teacher correlated the math test scores and scores on a motivation scale for her 9th graders. She was delighted to find a high correlation between the two sets of scores. Later in the semester she correlated the math test scores of mathematically gifted students who had math scores above 85th percentile and their motivation scores. She found a much lower correlation. What could be the reason for the low correlation? (1 POINT)
3. Suppose that a performance test of manual dexterity has been administered to three groups of subjects in different occupations. The data appear in the table below. Answer the following questions.
Group1
Group2
Group3
22
23
27
25
26
24
27
28
23
28
22
23
23
27
27
25
26
26
24
23
22
24
27
28
25
27
25
26
25
23
25
23
23
24
28
26
26
27
25
25
25
27
26
27
27
25
27
26
25
28
25
26
24
24
24
28
25
3.1. Compute the mean, mode, median, variance, and standard deviation for each group. (1 POINT)
3.2. Graph the histograms. (1 POINT)
3.3. Which group seems to have performed best on the test? (1 POINT)
3.4. Which group appears to be the most homogeneous in terms of manual dexterity? (1 POINT)
4. Thirty eighth grade students were selected from a class of a rural school. A researcher was able to obtain students’ math scores in 7th grade, the teacher’s evaluation scores on students’ academic aptitudes in 8th grade, and students’ final math scores in 8th grade. See the following table for data.
Math scores in 7th grade
Final math scores in 8th grade
Teacher evaluation score
75
43
4
76
44
4
68
36
1
66
38
2
73
41
2
71
40
2
55
27
1
72
46
5
61
38
2
68
35
2
64
31
2
76
42
3
71
45
4
73
41
4
78
45
5
71
41
3
86
50
5
55
34
3
96
51
4
96
54
4
50
28
2
81
50
5
58
37
3
90
46
4
58
23
3
77
45
3
88
55
5
65
34
3
77
54
3
75
54
4
4.1. Run a correlation analysis to examine the relationships among the three variables and interpret the results. (2 POINTS)
5. Given a normal distribution of scores with mean equal to 300 and variance equal to 100, answer the following questions.
5.1. What proportion of scores would fall below 280? (1 POINT)
5.2. What is the probability that a randomly picked score would fall between 310 and 320? (1 POINT)
6. A psychologist rejected the null hypothesis that there is no difference between freshmen and sophomores on drinking behavior. She used a significance level of .05 ( = .05) what is the probability ...
Case study analysis using Regression to determine which variables effect University Ranking based on ANOVA output values. Comparison of the predicted rank versus the actual ranking received.
STAT 200 Final ExaminationFall 2016 OL1US1Page 9 of 9STAT 200.docxwhitneyleman54422
STAT 200 Final ExaminationFall 2016 OL1/US1Page 9 of 9
STAT 200 Introduction to Statistics Name______________________________
Final Examination: Fall 2016 OL1/US1 Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
Answer all 20 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from calculators, programs or software packages without explanation will not be accepted. If you need to use technology to aid in your calculation, you have to cite the source and explain how you get the results. For example, state the Excel function along with the required parameters when using Excel; describe the detailed steps when using a hand-held calculator; or provide the URL and detailed steps when using an online calculator, and so on.
Show all supporting work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed. It is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. Your exam will receive a zero grade unless you complete the following honor statement.
Please sign (or type) your name below the following honor statement:
I understand that it is a violation of the UMUC Academic Dishonesty and Plagiarism policy to use unauthorized materials or work from others. I promise that I did not discuss any aspect of this exam with anyone other than my instructor. I further promise that I neither gave nor received any unauthorized assistance on this exam, and that the work presented herein is entirely my own.
Name _____________________Date___________________
Record your answers and work.
Problem Number
Solution
1
Answer:
(a)
(b)
(c)
(d)
(e)
Justification:
2
Answer:
(a)
(b)
(c)
Justification:
3
Answer:
(a)
(b)
Justification:
4
Answer:
(a)
IQ Scores
Frequency
Relative Frequency
50 - 69
23
70 - 89
249
90 -109
0.450
110 - 129
130 - 149
25
Total
1000
(b)
(c)
Work for (a) and (b):
5
Answer:
(a)
(b)
(c)
Justification:
6
Answer:
(a)
(b)
Work for (a) and (b):
7
Answer:
(a)
(b)
Work for (b):
8
Answer:
(.
STAT 200 Final Examination Fall 2014 OL4 US2 Page 1 of 12 .docxdessiechisomjj4
STAT 200 Final Examination Fall 2014 OL4 / US2 Page 1 of 12
Stat 200 Introduction to Statistics Name______________________________
Final Examination: Fall 2014 OL4 / US2 Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work
on the exam, and you may use a calculator.
Record your answers and work in this document.
Answer all 30 questions. Make sure your answers are as complete as possible. Show all of
your work and reasoning. In particular, when there are calculations involved, you must
show how you come up with your answers with critical work and/or necessary tables.
Answers that come straight from programs or software packages will not be accepted.
When requested, show all work and write all answers in the spaces allotted on the following
pages. You may type your work using plain-text formatting or an equation editor, or you may
hand-write your work and scan it. In either case, show work neatly and correctly, following
standard mathematical conventions. Each step should follow clearly and completely from the
previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither collaboration nor consultation with
others is allowed. Your exam will receive a zero grade unless you complete the following
honor statement.
Please sign (or type) your name below the following honor statement:
I promise that I did not discuss any aspect of this exam with anyone other than my instructor. I
further promise that I neither gave nor received any unauthorized assistance on this exam, and
that the work presented herein is entirely my own.
Name _____________________ Date___________________
STAT 200 Final Examination Fall 2014 OL4 / US2 Page 2 of 12
Record your answers and work.
Problem
Number
Solution
1
(25 pts)
Answers:
(a)
(b)
(c)
(d)
(e)
Work for (a), (b), (c), (d) and (e):
2
(5 pts)
Answer:
Work:
STAT 200 Final Examination Fall 2014 OL4 / US2 Page 3 of 12
3
(5 pts)
Answer:
Work:
4
(5 pts)
Answer:
Work:
5
(10 pts)
Answer:
Work:
STAT 200 Final Examination Fall 2014 OL4 / US2 Page 4 of 12
6
(10 pts)
Answer:
Work:
7
(5 pts)
Answer:
Work:
8
(5 pts)
Answer:
Work:
STAT 200 Final Examination Fall 2014 OL4 / US2 Page 5 of 12
9
(10 pts)
Answer:
Work:
10
(10 pts)
Answer:
Work:
11
(5 pts)
Answer:
Work:
12
(10 pts)
Answer:
Work:
STAT 200 Final Examination Fall 2014 OL4 / US2 Page 6 of 12
13
(10 pts)
Answer:
Work:
14
(5 pts)
Answer:
Work:
15
(5 pts)
Answer:
Work:
16
(5 pts)
Answer:
Work:
STAT 200 Final Examination Fall 2014 OL4 / US2 Page 7 of 12.
STAT 225 Final ExaminationSummer 2015 OL1US1Page 1 of 10STAT .docxdessiechisomjj4
STAT 225 Final ExaminationSummer 2015 OL1/US1Page 1 of 10
STAT 225 Introduction to Statistical Methods for the Behavioral Science
Final Examination: Summer 2015 OL1 / US1Name______________________________
Instructor __________________________
Answer Sheet
Instructions:
This is an open-book exam. You may refer to your text and other course materials as you work on the exam, and you may use a calculator.
Record your answers and work in this document.
Answer all 25 questions. Make sure your answers are as complete as possible. Show all of your work and reasoning. In particular, when there are calculations involved, you must show how you come up with your answers with critical work and/or necessary tables. Answers that come straight from programs or software packages will not be accepted. If you need to use software (for example, Excel) and /or online or hand-held calculators to aid in your calculation, please cite the source and explain how you get the results.
When requested, show all work and write all answers in the spaces allotted on the following pages. You may type your work using plain-text formatting or an equation editor, or you may hand-write your work and scan it. In either case, show work neatly and correctly, following standard mathematical conventions. Each step should follow clearly and completely from the previous step. If necessary, you may attach extra pages.
You must complete the exam individually. Neither collaboration nor consultation with others is allowed. Your exam will receive a zero grade unless you complete the following honor statement.
Please sign (or type) your name below the following honor statement:
I promise that I did not discuss any aspect of this exam with anyone other than my instructor. I further promise that I neither gave nor received any unauthorized assistance on this exam, and that the work presented herein is entirely my own.
Name _____________________Date___________________
Record your answers and work.
Problem Number
Solution
1
(25 pts)
Answers:
(a)
(b)
(c)
(d)
(e)
Work for (a), (b), (c), (d) and (e):
2
(5 pts)
Answer:
Study Time (in hours)
Frequency
Relative Frequency
0.0 – 4.9
5
5.0 - 9.9
13
10.0 - 14.9
0.22
15.0 -19.9
42
20.0 – 24.9
Total
100
Work:
3
(5 pts)
Answer:
Work:
4
(5 pts)
Answer:
Work:
5
(5 pts)
Answer:
Work:
6
(5 pts)
Answer:
Work:
7
(10 pts)
Answer:
Work:
8
(5 pts)
Answer:
Work:
9
(5 pts)
Answer:
Work:
10
(5 pts)
Answer:
Work:
11
(5 pts)
Answer:
Work:
12
(10 pts)
Answer:
Work:
13
(10 pts)
Answer:
Work:
14
(5 pts)
Answer:
Work:
15
(15 pts)
Answer:
(a)
x
P(x)
0
1
2
3
(b) mean = __________ , and standard deviation = _____________
Work for (a) and (b):
16
(20 pts)
Answer:
(a)
(b)
(c)
Work for (a), (b) and (c) :
17
(10 pts)
Answer:
Work:
18
(5 pts)
Answer:
Work:
19
(5 pts)
Answer:
Work:
20
(10 pts)
Answer:
Work:
21
(15 pt.
Running head Statistics Project, Part 2 Descriptive Statistics.docxtoltonkendal
Running head: Statistics Project, Part 2: Descriptive Statistics and Hypothesis
2
Statistics Project, Part 2: Descriptive Statistics and Hypothesis
Marcela Montoya
PSYCH 625
Dr. Washington
November 16, 2017
Statistics
Age
Math Score
Reading Score
Total Score
N
Valid
50
50
50
50
Missing
0
0
0
0
Mean
32.02
75.00
75.78
150.78
Std. Error of Mean
.614
1.793
1.633
3.044
Std. Deviation
4.340
12.675
11.550
21.522
Variance
18.836
160.653
133.400
463.196
Skewness
.189
-.699
-.793
-.803
Std. Error of Skewness
.337
.337
.337
.337
Histogram
H0: The Total score is proportional to the math score
H1: Anything else.
We reject the null hypothesis since the math test scores do not seem to have an effect on the total scores. The normal curves of both the math scores and total score are different. The skewness of the math score is also less than the skewness of the total score -.699<-.803.
Running head: COMPARING MEANS
1
COMPARING MEANS
2Statistics Project, Part 3: Comparing Means
Marcela Montoya
PSYCH 625
Dr. Washington
November 26, 2017
ONEWAY College TestPrep BY MathScore
/MISSING ANALYSIS.
ANOVA
Sum of Squares
df
Mean Square
F
Sig.
College
Between Groups
36.583
29
1.261
1.813
.085
Within Groups
13.917
20
.696
Total
50.500
49
Test Prep
Between Groups
18.667
29
.644
3.358
.003
Within Groups
3.833
20
.192
Total
22.500
49
H0 : Math score is influenced with the level of college vs.
H1 : Math score is not influenced with level of college
H0 : Math score is influenced with level of test preparation vs.
H1 : Math score is not influenced with level of college
We notice that the level of college does not influence the math score since the level of significance is greater than 0.05
The level of test preparation influenced the math score since the level of significance is less than 0.05.
Running head: Statistics Project, Part 1: Importing Data into IBM SPSS Software 1
Frequencies Table
College
no college
some college
Caffeine
Caffeine
yes
no
yes
no
Count
Count
Count
Count
Gender
Male
Test Prep
no preparation
3
0
3
0
moderate preparation
2
0
1
1
high preparation
0
0
0
1
Female
Test Prep
no preparation
3
1
1
1
moderate preparation
1
0
4
1
high preparation
0
0
1
0
College
associate's degree
bachelor's degree
Caffeine
Caffeine
yes
no
yes
no
Count
Count
Count
Count
Gender
Male
Test Prep
no preparation
0
0
0
0
moderate preparation
5
1
2
1
high preparation
1
2
1
0
Female
Test Prep
no preparation
1
0
1
0
moderate preparation
6
0
2
0
high preparation
1
0
2
0
The number of males that had no preparation in the test took caffeine. Those who had moderate preparation only three did not take caffeine, which were one from some college, one from associate’s degree and one from bachelor’s degree. Majority of males had moderate preparation were under associates degree and bachelor’s degree and most took caffeine. There is a low number of males who had high preparations and majority of the ...
2. Title: To analyze and compare the
performance of Mathematics and
Applied Statistics for Year 1 & 2 at
EASTC in 2011.
2
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.
3
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
4
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
6
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.
7
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
8
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
11
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
12
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.
13
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
14
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.
15
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.
17
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)
18
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.
19
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
20
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.
21
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.
22