This document provides information about a student project investigating how engagement in extracurricular activities affects academic performance. It includes the project title, purpose, data collection methods, presentation of collected data through tables and graphs, analysis using measures of central tendency, probability, chi-square test, and correlation. The analysis found a low negative correlation between time spent on extracurricular activities and academic performance. The document concludes there is a slight decrease in grades as time on extracurricular activities increases.
This School Based Assessment was made to fulfill Samantha's Social Studies Course for the Caribbean Secondary Education Certificate. Please do not plagiarize this document in any way. This is solely for the purpose of helping others to improve their grades as a Caribbean student.
English SBA for CSEC. *The file has been protected and has been submitted to CXC. Do not copy as the digital signature of the file cannot be removed or edited. Use as a guide only
This document is meant to be used as a guide to current and upcoming students at the CXC CSEC level experiencing difficulty in doing their School Bases Assesment (SBA). This document follows the 2010 syllabus which may be subject to change.
This School Based Assessment was made to fulfill Samantha's Social Studies Course for the Caribbean Secondary Education Certificate. Please do not plagiarize this document in any way. This is solely for the purpose of helping others to improve their grades as a Caribbean student.
English SBA for CSEC. *The file has been protected and has been submitted to CXC. Do not copy as the digital signature of the file cannot be removed or edited. Use as a guide only
This document is meant to be used as a guide to current and upcoming students at the CXC CSEC level experiencing difficulty in doing their School Bases Assesment (SBA). This document follows the 2010 syllabus which may be subject to change.
Human & Social Biology - Sample Project on 'The Impact of Heath Practices on ...Raheme Matthie
H.S.B research that was carried out on The Impact of Heath Practices on the Environment. This will help to guide you as to how you should go about doing this assignment.
CSEC Business Cognate SBA Research GuidelinesDebbie-Ann Hall
This document seeks to guide users in their attempt to satisfy the requirements for the SBA. It provides examples which were generated by participants in Teacher Orientation Workshops conducted by the Caribbean Examinations Council in May – June 2017 across the Region in collaboration with the Ministries of Education.
this is a very good example of a POB sba I have gain a grade one (1) this will help you to gain that as well.... you can ask me for help on facebook @ dwayne the new version
This documents is a Caribbean History School Based Assessment that covers the topic: Is it fair to say that the Chinese and Indian immigrants solved the labour problem after 1838?
Human & Social Biology - Sample Project on 'The Impact of Heath Practices on ...Raheme Matthie
H.S.B research that was carried out on The Impact of Heath Practices on the Environment. This will help to guide you as to how you should go about doing this assignment.
CSEC Business Cognate SBA Research GuidelinesDebbie-Ann Hall
This document seeks to guide users in their attempt to satisfy the requirements for the SBA. It provides examples which were generated by participants in Teacher Orientation Workshops conducted by the Caribbean Examinations Council in May – June 2017 across the Region in collaboration with the Ministries of Education.
this is a very good example of a POB sba I have gain a grade one (1) this will help you to gain that as well.... you can ask me for help on facebook @ dwayne the new version
This documents is a Caribbean History School Based Assessment that covers the topic: Is it fair to say that the Chinese and Indian immigrants solved the labour problem after 1838?
Researchers use several tools and procedures for analyzing quantitative data obtained from different types of experimental designs. Different designs call for different methods of analysis. This presentation focuses on:
T-test
Analysis of variance (F-test), and
Chi-square test
Identify each of the following as examples of nominal, ordinal, inte.docxscuttsginette
Identify each of the following as examples of nominal, ordinal, interval, or ratio scales of measurement. (4 points each)
A poll of registered voters in Florida asking which candidate they support
The length of time required for a wound to heal when using a new medicine
The number of telephone calls arriving at a switchboard per five-minute period
The distance first-year college football players can kick a ball
Mental health diagnoses present in an elderly population
The rankings of employees on their job performance
(Points : 24)
Question 2.
2.
Two hundred raffle tickets are sold. Your friend has five people in her family who each bought two raffle tickets. What is the probability that someone from her family will win the raffle?
(Points : 4)
Question 3.
3.
Jolie has 45 minutes to do her statistics homework. If the mean is 38 minutes and the standard deviation is 3, calculate Jolie's z score. Once calculated, interpret your findings in terms of Jolie's performance.
(
HINT:
use the normal distribution and the probability that other students performed better or worse.) (Points : 8)
Question 4.
4.
A psychologist measures units of change for a memory test after students are given an opportunity to sleep only four hours. The following change units were obtained: 7, -12, 4, -7, 3, -10. Find the a) mean, b) median, c) mode, d) standard deviation, e) range, and f) variance. (Points : 24)
Question 5.
5.
A student scored 81 on a chemistry test and 75 on a history test. For the chemistry test, the mean was 70 and the standard deviation was 20. For the history test, the mean was 65 and the standard deviation was 8. Did the student do better on the chemistry test or the history test? Explain your answer. (Points : 12)
Question 6.
6.
Suppose you want to figure out what to do with your degree in psychology. You ask some fellow students from your psychology program who recently graduated to find out what they are doing with their degree and how much it pays. What type of sampling is this? What are the limitations of this sampling approach? (Points : 8)
Question 7.
7.
Variables in which the values are categories are known as (Points : 4)
Interval variables
Nominal variables
Ordinal variables
Ratio variables
Question 8.
8.
Before the researcher can conduct a statistical test, the research question must be translated into (Points : 4)
A testable hypothesis
Additional observations
Mathematical symbols
Numbers
Question 9.
9.
The hypothesis stating that there are no differences, effects, or relationships is (Points : 4)
The alternative hypothesis
The baseline hypothesis
The null hypothesis
The reasonable hypothesis
Question 10.
10.
A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the mean score? (Points : 4)
6.6.
Distinguish between Parameter and Statistic.
Calculate sample variance and sample standard deviation.
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This is my statistics exam I need help I have been lost this whole s.docxdivinapavey
This is my statistics exam I need help I have been lost this whole semester
Identify each of the following as examples of nominal, ordinal, interval, or ratio scales of measurement.
1.Identify each of the following as examples of nominal, ordinal, interval, or ratio scales of measurement.
1. A poll of registered voters in Florida asking which candidate they support
2. The length of time required for a wound to heal when using a new medicine
3. The number of telephone calls arriving at a switchboard per five-minute period
4. The distance first-year college football players can kick a ball
5. Mental health diagnoses present in an elderly population
6. The rankings of employees on their job performance
2) Two hundred raffle tickets are sold. Your friend has five people in her family who each bought two raffle tickets. What is the probability that someone from her family will win the raffle?
3) Jolie has 45 minutes to do her statistics homework. If the mean is 38 minutes and the standard deviation is 3, calculate Jolie's z score. Once calculated, interpret your findings in terms of Jolie's performance.
4) . A psychologist measures units of change for a memory test after students are given an opportunity to sleep only four hours. The following change units were obtained: 7, -12, 4, -7, 3, -10. Find the a) mean, b) median, c) mode, d) standard deviation, e) range, and f) variance.
5) A student scored 81 on a chemistry test and 75 on a history test. For the chemistry test, the mean was 70 and the standard deviation was 20. For the history test, the mean was 65 and the standard deviation was 8. Did the student do better on the chemistry test or the history test? Explain your answer
6. Suppose you want to figure out what to do with your degree in psychology. You ask some fellow students from your psychology program who recently graduated to find out what they are doing with their degree and how much it pays. What type of sampling is this? What are the limitations of this sampling approach?
7. Variables in which the values are categories are known as)
Interval variables
Nominal variables
Ordinal variables
Ratio variables
8. Before the researcher can conduct a statistical test, the research question must be translated into
A testable hypothesis
Additional observations
Mathematical symbols
Numbers
9. The hypothesis stating that there are no differences, effects, or relationships is)
The alternative hypothesis
The baseline hypothesis
The null hypothesis
The reasonable hypothesis
10. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the mean score?
6.6
7.2
7.8
8.7
11. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 10} What is the median score?
6
7
8
9
12. A group of students made the following scores on a 10-item quiz in psychological statistics: {5, 6, 7, 7, 7, 8, 8, 9, 9, 10, 1.
1. What type of research uses numeric measurement data (Points .docxpaynetawnya
1. What type of research uses numeric measurement data? (Points : 3)
2. What type of research uses a research hypothesis? (Points : 3)
3. What type of research does not use statistical data analysis? (Points : 3)
4. What type of research preempts all other types of research endeavors? (Points : 3)
5. Business research is a type of ________________ inquiry. (Points : 3)
6. What are the three main types of non-probability sampling used in business research? (Points : 3)
7. In a situation where in a confidence level .01 what percent of the measurement results are left to chance? (Points : 3)
8. What is the most important ingredient in a statistical testing procedure? (Points : 3)
9. If a production manager wanted to determine whether or not the first shift was processing more widgets than the second shift, what type of statistical process would be used? (Points : 3)
10. What type of t test seeks to determine whether or not a relationship exists in one sample over two conditions? _______________ (Points : 3)
11. Which of the examples below represent the Ratio level of scaling?
A) A high temperature of 83 degrees Fahrenheit
B) A survey result that 24 students work full time, 36, part time.
C) Bill is consistently rated most effective communicator of his group.
D) Gallup says that 60% of the voters support the incumbent.
E) Pick up three pounds of ground beef please.
F) Patty acts as expected based on her first-born family position.
G) Seattle at an altitude of 67 feet is higher than Death Valley at an altitude of – 120.
H) The door is 37 inches wide, the door frame is 36 inches wide.
(Points : 3)
B, C and F
D, E and G
C, F and H
A, E and H
12. Select those issues that only relate to selecting a specific statistical test. (Do not select items common to all tests or not applying to statistical tests.) (Points : 3)
The distribution (shape) of the population (e.g., normal, skewed, flat, etc.)
The measurement scale/nature of the data being evaluated (nominal, ordinal, interval or ratio)
The size of the population (assuming it is much larger than any samples)
The level of significance (_) you wish to place on the test results
Whether you have matched/related or unmatched/unrelated samples
The degrees of freedom (sample size) associated with your sample(s)
The statement of the null and research hypotheses
Whether the sample was stratified or not
13. Which of the following apply to Populations?
A) parameter
B) “Roman” letters, i.e.: x, s
C) A bounded, defined complete group (people, objects, etc.) having something in common to be described in its totality
D) “Greek” letters, i.e.: μ, σ
E) One or more subsets of a larger defined group, used to represent the larger group
F) 170 Republicans selected randomly from King County voter records
G) All Democrats in the state of Washington (totality)
(Points : 3)
A, B ...
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Elementary Statistics Practice Test 1
Module 1: Chapters 1-3
Chapter 1: Introduction to Statistics.
Chapter 2: Exploring Data with Tables and Graphs.
Chapter 3: Describing, Exploring, and Comparing Data.
The International Journal of Engineering and Science (The IJES)theijes
The International Journal of Engineering & Science is aimed at providing a platform for researchers, engineers, scientists, or educators to publish their original research results, to exchange new ideas, to disseminate information in innovative designs, engineering experiences and technological skills. It is also the Journal's objective to promote engineering and technology education. All papers submitted to the Journal will be blind peer-reviewed. Only original articles will be published.
Running head Statistics 2Statistics Statistics Na.docxagnesdcarey33086
Running head: Statistics
2
Statistics
Statistics
Name:
Course:
Instructor:
Institution:
Date of Submission:
Assignment #4: Model Diagnostics
A fundamental requirement in the classical linear regression is that the regression error term must be normally distributed with zero mean and constant variance (Greene, 2008). The normality tests results are presented below.
All the plots have values greater than the threshold probability value of 0.05 thus the null hypothesis of normality of the regression residuals could not be rejected at 5 per cent significance level. Conclusion is thus made that the regression residuals from the estimated equations followed a normal distribution. Since any linear function of normally distributed variables is considered to be normally distributed, normal distribution of the residuals had the implication that the coefficients of the estimates were also themselves normally distributed (Gujarati, 2008).
The residual plot is shown below:
From the residual plot it can be seen that all the residuals fall within the standard error bands thus confirming that the model is stable and can thus be used for forecasting.
References
Greene, W. (2008). Econometric analysis, 6th ed. . New Jersey: Pearson-Prentice Hall.
Gujarati, D. (2004). Basic econometrics 4th ed. . New York: McGraw Hill Companies.
Normal Probability Plot
2.6315789473684208 7.8947368421052602 13.15789473684211 18.421052631578942 23.684210526315791 28.947368421052641 34.21052631578948 39.473684210526301 44.73684210526315 50 55.26315789 4736857 60.526315789473699 65.789473684210563 71.052631578947384 76.315789473684163 81.578947368420984 86.842105263157904 92.105263157894726 97.368421052631547 10.7 11.3 11.8 11.9 12 12 12 12.4 12.5 12.6 13.1 13.2 13.4 13.5 13.5 14.2 14.5 14.5 14.6
Sample Percentile
MedianSchoolYears
Age Residual Plot
60 30 62 44 0 30 62 68 46 56 36 28 0 0 34 26 52 50 44 0.50878516451792 1.7144464705013149 -0.42159945482941003 0.54117037792769895 0.71299080887547295 1.269413932725179 0.26951686627728799 0.22131431339594501 -0.13472012994437299 0.22075061567252199 -1.3199768562363781 -0.18681496091028299 0.380020030213299 -1.451131014273024 -0.56052688701790399 -0.116260966970037 -0.67291294283960901 -0.49015761805784802 -0.48430774902780499
Age
Residuals
RUNNING HEADER: WEEK 3 ASSIGNMENT 4 1
WEEK 3 ASSIGNMENT 4 13
Week 3 Assignment 4
Introduction
In this project I selected six variables from the ' SampleDataSet.xlsx'. Among these six variables three of them were continuous and the reaming three were discrete variables. The continuous variables selected for this study are Age, WealthScore and MedianSchoolYears. The discrete variables selected for this study are NumberOfChildren, MailResponder and NumberOfCars.
Analysis
Age
The age is a continuous variable which takes only positive values even though we usually consider the integer part of it. The descriptive statistics summary of the age variable .
UNIT 3
SUCCESS GUIDE
1 | GB 513 Unit 3 Success Guide v.6.13.17
UNIT 3 SUCCESS GUIDE
This unit is the other “most difficult” one. Hypothesis testing has two parts: setting-up
the hypotheses and calculating the critical values to determine results. They both
pose difficulty for a lot of students. The seminar will be on the first and the recorded
lecture will be on the second. You need to make sure you understand both,
otherwise you will not be able to get to the right conclusions.
1. As always, start by reading the chapters and studying the solved examples.
2. Watch the lecture video in document sharing. It focuses on why we do
hypothesis testing, how to do it with Excel and solves two sample problems.
3. Watch this from Khan Academy:
https://www.khanacademy.org/math/statistics-probability/significance-
tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-
values
This one talks more about how to write the null and alternative hypotheses
(which a lot of students get wrong) and also solves the problem using
formulas.
4. Watch the sample problem solutions in Course Resources.
5. If you still want more videos, search YouTube for “hypothesis testing.” Several
introductory level videos are available, such as
https://www.youtube.com/watch?v=HmMjS88eSVE and
https://www.youtube.com/watch?v=0zZYBALbZgg
Email your instructor if you find any of these links to be broken.
Avoid these mistakes!
GENERAL NOTES
RESOURCES
COMMON MISTAKES IN THE ASSIGNMENT
https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-values
https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-values
https://www.khanacademy.org/math/statistics-probability/significance-tests-one-sample/tests-about-population-mean/v/hypothesis-testing-and-p-values
http://www.youtube.com/watch?v=HmMjS88eSVE
http://www.youtube.com/watch?v=HmMjS88eSVE
http://www.youtube.com/watch?v=HmMjS88eSVE
http://www.youtube.com/watch?v=0zZYBALbZgg
http://www.youtube.com/watch?v=0zZYBALbZgg
http://www.youtube.com/watch?v=0zZYBALbZgg
2 | GB 513 Unit 3 Success Guide v.6.13.17
Students commonly get the null and alternative hypotheses reversed, or
get them completely wrong.
Students also commonly do not state the hypothesis fully. This is correct:
“null hypothesis: there is no difference between the average salary for
group 1 and the average salary of group 2.” This is not sufficient: “ho:
x1=x2”
Students sometimes compare the averages of the two groups and base
their determination on which one is greater, rather than properly doing a
hypothesis test.
Students sometimes do the calculations correctly, but do not write out
what the conclusion is. This is correct: “We therefore reject the null
hypothesis, which means we conclude that there i ...
2. 2
Table of Content
Project title…………………………………………………………………………………..3
Purpose of project……………………………………………………………………………4
Method of data collection……………………………………………………………………5
Presentation of data………………………………………………………………………….6-11
Analysis of data……………………………………………………………………………...12-19
Discussion of findings……………………………………………………………………….20-23
Glossary ……………………………………………………………………………………..24
Reference…………………………………………………………………………………….25
Appendix……………………………………………………………………………………..26-29
3. 3
PROJECT TITLE
To investigate and to find out the causes of student
engaging in an extracurricular activity and how it affect
their academic performance.
4. 4
PURPOSE OF PROJECT
Extracurricular activities are activities performed by student that fall outside the realm of
the normal curriculum of school or university. Such activities are generally voluntary as opposed
to mandatory, non-paying, social, and philanthropic as opposed to scholastic and often involve
others of the same age group.
It has been observed that the time the student spend in extracurricular activity affect the
student overall school average. Therefore the researcher choose this topic to find out if the
number of hours spent in extracurricular activity affect their performance.
The benefits of doing this research is that data will be analyze on the student
extracurricular activity and the problem will be recognized. The source will be student from
various clubs. Another benefits is that alternative solution will be made for the student to the
problem they are facing.
5. 5
METHOD OF DATA COLLECTION
The St. Mary High School has a population (N) of over fifteen hundred students. A
sampling frame of 275 students, consisting of only grade 8 students was chosen for the
observation due to the similarities in the subjects done by these students. A sample (n) of 30
students was selected to carry out this investigation. Data was collected by the use of
questionnaire and observation.Questionnaire allows for firsthand information, they are easily
administered and they are less time consuming. A random sample of 30 students was taken
which consist of 5 students from each class. On the other hand, observation gives the researcher
the ability to gather extra information with persons knowing.
The method of data collection was judged to be appropriate due to the fact that the
questions can be structured to gather only the information necessary for the investigation. There
were no flaws because the questionnaires were given to randomly chosen respondents so as to
prevent bias. In addition, the questions were clearly stated to prevent confusion so that they
could be easily answered.
The researcher was carried out on the January 15, 2013. Thirty (30) questionnaires were
given out to the students that were randomly chosen for the investigation and all were completed
and returned.
7. 7
Figure1: Table showing number of respondents and their gender.
Sex Number of Respondents
Male 12
Female 18
The table above shows the gender of the respondents who were chosen for the investigation.
8. 8
The above bar graph shows the number of students which is in a extracurricular activity. There
were twenty (20) student who engage in track and field, eight (8)student who engage in cadet
and two (2) student who engage in quiz.
20
8
2
0
5
10
15
20
25
track&field cadet quiz
Number
of
students
Types of Social Networks
Figure 2: Bar graph showing the number of
students who engage in the various club
quiz
cadet
track&field
9. 9
The above diagram shows the average number of hours spent students on the various clubs.The
average number hours spent in track and field by students weekly is eight (8) hours, cadet
accounted for five (5) hours while only three (3) hours was spent in quiz.
0
1
2
3
4
5
6
7
8
track&field
cadet
quiz
8
5
3
Hours
Social Networks
Figure 3: Bar graph showing the average
number of hours spent in each club weekly
track&field
cadet
quiz
10. 10
The above diagram shows the percentage of students who chose the various reasons for them
engaging in extracurricular activity. Fifty percent (50%) said that they engage in the club for
communication, twenty percent (20%) said leisure and trend while ten percent (10%) replied
personal benefits.
50%
20%
20%
10%
Figure 4: Pie chart showing reasons of
students for using social networks
Communication
Leisure
Trend
personal benefits
11. 11
The figure above shows the average number of hours spent studying based on the type of
extracurricular activity the student engage in frequently. The students who engage in track and
field spend an average of four(4) hours studying, students who engage in cadet spend an average
of six (6) hours studying and those who engage in quiz spend an average of nine (9) hours
studying.
track&field
cadet
quiz
0
1
2
3
4
5
6
7
8
9
track&field
cadet
quiz
4
6
9
Number
of
hours
spent
studying
social networks
Figure 5: Conical graph showing the number
of hours spent studying
track&field
cadet
quiz
13. 13
CENTRAL TENDENCY
The figures below show the average grade for the students during the End of Term Exams 2011.
They are as follows:
38% 50% 52% 55% 56% 57% 58% 60% 62% 63% 65% 66%
68% 70% 72% 74% 75% 80% 80% 80% 80% 81% 82% 83%
84% 84% 85% 86% 87% 93%
Mean
=
=2126/30
=70.87%
Mean average of students in Term Exams 2011 = 70.87%
Mode
Mode= 80%
The most frequent average grade scored in exams = 80%.
Median
Median position= ½(n+1)th
=1/2(30+1th
=1/2(31)th
=15.5
=16th
16th
position = 74%
14. 14
PROBABILITY
Conditional Probability
In order to ascertain the needed data about whether or not the number of hours spent in
extracurricular activity affect the performance of the students in the exams, the researcher saw it
necessary to conduct a probability test using conditionalprobability.
Let G be the event that a student obtained an average grade of below 60% in the exam.
Let H be the event that a student spent an average of 8 hours in an extracurricular activity.
P (G/H) = P (GnH) = (5/30)= 0.167 = 0.2503 = 167/667
P(H) (20/30) 0.667
Let G be the event that a student obtained an average grade of below 60% in the exam.
Let H be the event that a student spent an average of 8 hours in an extracurricular activity
P (G/H) = P (GnH) = (15/30) = 0.50 = 0.7463 = 50/67
P (H) (20/30) 0.67
15. 15
Chi- Square Test
The grades used below are the average grades of the students observed. They are described as
low (below 51%), medium (between 50% and 80%) and high (above 79%). The average number
of hours spent in an extracurricular activity was also used.
Time (avg.) 2 5 8 Total
Low 0 1 1 2
Medium 0 3 12 15
High 2 4 7 13
Total 2 8 20 30
Table showing the hours spentin an extracurricular activity by students and their average grades.
Time (avg.) 2 5 8 Total
Low 0.133 0.533 1.333 2
Medium 1 4 10 15
High 0.867 3.467 8.667 13
Total 2 8 20 30
Contingency table
16. 16
Expected Frequency = Row total * Column total
Grand total
Ho: The average grades obtained by students in their end of term exams and the number of hours
spent in extracurricular activity are independent variables.
H 1: The average grades obtained by students in their end of term exams and the number of hours
spent in an extracurricular activity are not independent variables.
Row * Column
ν = (3-1) * (3-1)
= 2*2
= 22
= 4
x2
= 4.159
ᵡ2
5% (4) = 9.488
O E (O-E)2
E
0 0.133 0.133
0 1 1
2 0.867 1.481
1 0.533 0.409
3 4 0.25
4 3.467 0.082
1 1.333 0.083
12 10 0.4
7 8.667 0.321
∑O=30 ∑E=30 ∑(O-E)2
= 4.159
E
17. 17
Since x2
= 4.159 <ᵡ2
5% (4) = 9.488, we do not reject Ho and conclude that the average grade
obtained by students and the average number of hours spent in an extracurricular activity are
independent.
Correlation and Linear regression graph
Y= average grade obtained in exam.
X=number of hours spent in an extracurricular activity.
.
y = -1.714x + 82.52
R² = 0.056
0
10
20
30
40
50
60
70
80
90
100
0 2 4 6 8 10
averagegradeinexam(%)
time spent in extra curicular activity (hrs)
Average grade
Average grade
Linear (Average grade)
22. 22
According to Fligner (2006) “Observation studies are investigations in which one simply
observes the state of some population, usually with data collected by sampling. Even with proper
sampling, data from observational studies are generally not appropriate for investigation cause-
and –effect relations between variables”.
The investigation gave significant information about the relationship between the
performance of students and the average time spentin an extracurricular activity.
It was found out that the average grade the student observed was 70.87%. After
examining this data more closely, it was seen that 53.33% of the students observed scored above
the average grade. On further observation, the modal average was found to be 80% as it was the
average that was obtained the most. The central average amount was found to be 74%, this
revealed that 50% of the student observed scored 74% or below and also that 50% were scoring
74% or above.
A probability test was done to see if it was more likely for a student to spend greater
amount of hours in extracurricular activity and still obtain high grades or was it that students had
to spend less time in extracurricular activity to achieve these grade. After completing the test, it
was seen that the probability of a student scoring an average of 60% or above while spending an
average of 8 hours in extracurricular activity (0.7463 or 50/67) was significantly than the
probability of a student scoring an average of below 60% while spending an average of 8 hours
in an extracurricular activity (0.2503 or 167/667).
To test for the relationship/independence of the average grade and the average hours
spentin an extracurricular activity, a chi-squared test and correlation and linear regression graph
was done. The chi-squared test showed that at the 5% level of significance that the average grade
23. 23
obtained in the exam and the average number of hours spent on social networks is independent.
This is because x2
=4.159<ᵡ2
=9.488, therefore x2
would fall below the rejection region and
conclude that both variables are independent.
On the other hand, the correlation and linear regression graph revealed that there was a
very low negative relationship between the average grade obtained and the hours spentin an
extracurricular activity. This was given by the correlation coefficient=0.0264. The regression
coefficient -1.7143 represents the decrease in y for each unit increase in x, that is for every 1
hour increase in time the average grade obtained will decrease by 1.7143%. The constant of
82.524 represents the theoretical value of y when x=0.
24. 24
Conclusion
From the investigation it can be seen that there is a very low negative relationship between the
average grade obtained and the hours spentin an extracurricular activity. As was seen from the
calculations carried out, an increase in the hours spentin an extracurricular activity has a small
effect on the grades obtained as was shown by the regression coefficient of -1.7143.
Out of this investigation, it can be inferred that even though the students tend to score good
grades even though spending a large amount of time on social networks, the number of hours
spent in an extracurricular activity cause their grades to decrease slightly.
25. 25
Glossary
Symbols Meanings
∑ The sum of any values.
µ The mean value.
ᵡ2 The chi-square test value.
P The probability of any event.
O The observed frequency.
E The expected frequency.
(O-E)2
E
The test statistic.
ν The degrees of freedom of the test.
X2
The critical value (rejection region) of the test.
r The linear correlation coefficient
N Population size.
n Sample size.
26. 26
Reference
Fligner, M A. (2006). Introduction to the practice of statistics, New York, W. H. Freeman and
company.
28. 28
QUESTIONNAIRE
Dear Student,
I am a sixth form student at the Saint Mary High School who is currently studying
Applied Mathematics. This investigation is a requirement for a CAPE Applied Mathematics
school based assessment (SBA). The main objective of this questionnaire is to gather information
which is accurate and reliable. The researcher is asking for your cooperation in successfully
completing this questionnaire as your confidentiality is guaranteed.
Please circle the appropriate response.
Gender………………………………………
1. State your age:
……………………………………...
2. Do you engage in a extra-curricular activity?
a) yes
b) Sometimes
c) No
3. If yes, which type ofextra-curricular activity?
a) Track and Field
b) Cadet
c) Quiz
4. How long do you spend at the club weekly?
a) 0-2hrs
b) 3-4hrs
c) 5-6hrs
d) 7-8hrs
5. What is your reason for taking part in aextra-curricular activity?
a) Communication
b) Leisure
29. 29
c) trend
d) Personal benefit
6. How many hours do you spend studying?
a) 0-2hrs
b) 3-5hrs
c) 6-7hrs
d) 8-9hrs
7. What was your average grade for the End of Term Exams 2011?
a) 90% and over
b) 80-89%
c) 70-79%
d) 69% and under
8. Do you think that the amount of hours spent in extra-curricular activity have any effect
on your academic performance?
a) Yes
b) No
9. If yes, in what way?
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
10. What do you think can be done to curb this problem?
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
………………………………………………………………………………………………
11. How do you think the action stated above will help to fix the problem?
………………………………………………………………………………………………
………………………………………………………………………………………………