Statistical Techniques: Research Study Planning and Analysis

This assignment presents a series of hypothetical research studies designed to illustrate the application of various statistical techniques. The assignment covers independent samples t-tests, paired samples t-tests, and correlation analysis. For each study, the assignment details the research question, the variables involved, the nature of the collected data, and the rationale for selecting the specific statistical test. The studies explore diverse research scenarios, including comparing blood pressure between genders, analyzing height differences in students, examining mobile phone bill variations, and investigating SAT score disparities. Furthermore, the assignment includes studies on the effectiveness of medical treatments, training programs, and exercise regimes, along with analyses of the relationship between education, salary, and job satisfaction. Each study is meticulously planned to provide a clear understanding of how these statistical methods can be employed to address different research questions and analyze different types of data. The document provides a comprehensive overview of the application of statistical methods in research, offering valuable insights for students studying statistics and research methodology.

STATISTICAL TECHNIQUES
STUDENT ID:
[Pick the date]

Independent Sample T test
STUDY 1
 This hypothetical study would aim to determine if there is any significant difference in the
average blood pressure of males and females.
 There are essentially two pivotal variables which are of consideration for the hypothetical
study. One of these is the gender of the participant while the other would be the blood
pressure.
 The data would be collected by measuring the blood pressure of the selected sample which
would be representative of the underlying population.
 The research question is stated below.
“Is there any significant difference between the mean blood pressure for men and women?”
 The statistical test that would be used in the given case would be independent sample t test. It
is imperative that the blood pressure for the two genders is independent since the blood
pressure of one gender does not impact the blood pressure of the other. A t test would be
appropriate since the population standard deviation for the two samples (Eriksson &
Kovalainen, 2015).
STUDY 2
 The key objective is to determine if there is any significant difference between the height of
boys and girls studying in 10th grade of a given educational institution.
 The two variables of interest would be the height of boys and girls which would be
compared.
 The data collection would be facilitated by randomly selecting 25 boys and 25 girls from all
the grade 10 students enrolled in the given education institution.
 The research question is stated below.
“Is there any significant statistical difference between the height of boys and girls in the 10th
grade of the selected educational institution?”
 Considering that the heights of the two genders is independent of each other and also the
population standard deviation is not known, the independent samples t test is an appropriate
choice.
STUDY 3
 The key objective of the hypothetical study is to outline if there is any difference between the
average monthly mobile phone bill of male and female employees working at a particular
corporate organization.
 The two variables of interest would be the monthly mobile phone bills of male and female
employees in the selected organization.

 The data collection would be facilitated through a questionnaire which would aim at
recording the latest monthly mobile bill for employees belonging to different genders.
Consideration would be made in regards to selection of sample so that the two samples are
representative of respective populations in terms of key attributes of significance (Hillier,
2016).
 The research question is “Is there any significant statistical difference between the average
monthly mobile bills of male and female employees of the selected corporate organization?”
 Considering that the monthly mobile bills of the two genders is independent of each other
and also the population standard deviation is not known, the independent samples t test is an
appropriate choice.
STUDY 4
 The objective of this hypothetical study is to determine if the performance of male and
female student in SAT exam in 2017 is significantly different from each other or not.
 The key variables which are required for the given test would be the SAT score of male and
female candidates appearing for SAT in 2017.
 In order to obtain the requisite data, a sample of 50 male and 50 female candidates who have
appeared in SAT in 2017 would be obtained through questionnaire. The selected sample
would be obtained based on stratified sampling as key attributes may influence SAT scores
(Flick,2015).
 The research question is “Is there any significant statistical difference between the average
SAT score of male and female candidates for those who appeared in 2017”?
 Considering that the SAT scores in 2017 of the two genders is independent of each other and
also the population standard deviation is not known, the independent samples t test is an
appropriate choice.
STUDY 5
 The objective of the hypothetical study is to determine if the average time for preparation of
drink 1 exceeds the time for preparation of drink 2 at a given café.
 The key variables for this test would be the preparation time for drink 1 and drink 2.
 For obtaining the requisite data, sample data regarding the preparation time of the two drinks
need to be collected from the concerned café.
 The research question is “Whether the average time for drink 2 preparation exceeds the
corresponding average time for drink 1 preparation”?
 Considering that the SAT scores in 2017 of the two genders is independent of each other and
also the population standard deviation is not known, the independent samples t test is an
appropriate choice

Paired samples t test
STUDY 1
 This hypothetical study would aim to determine the efficiency of a new cancer drug which
results in lower growth of cancer cells in case of pancreatic cancer.
 There are essentially two key variables for the given study i.e. incidence of cancer cells in the
infected pancreas before and after administering the drug.
 A sample of 50 patients which are representative of population of pancreatic cancer would be
taken and observations would be made through biopsy before and after the drug,
 The research question is “Is there any significant decrease in the concentration of cancer cells
in pancreatic tumor after administering the new drug?”
 Considering that the sample remains the same for both the observations, hence the paired t
test would be suitable especially considering that the population standard deviation is
unknown for the samples (Lind, Marchal. &Wathen, 2015).
STUDY 2
 This hypothetical study would aim to determine the effectiveness of the training program
with regards to job satisfaction.
 There are essentially two key variables for the given study i.e. job satisfaction scores
measured on a scale of 1 to10 before and after training.
 Considering that there are a host of factors at play, hence in order to determine the effect of
training program, for the same sample employees (size 50), the job satisfaction scores before
the training and after the training would be recorded through internet based survey (Medhi,
2015).
 The research question is “Is there any significant increase in the job satisfaction score after
the training?”
 Considering that the sample remains the same for taking the before and after readings, hence
the paired t test would be suitable especially considering that the population standard
deviation is unknown for the samples.
STUDY 3
 This hypothetical study would aim to determine the effectiveness of a new exercise regime
on stamina.
 There are essentially two key variables for the given study i.e. stamina before the exercise
regime and stamina after the exercise regime. This stamina would be reflected by the time for
which non-stop running at a minimum speed of 6km/hr can be done.
 As the stamina of the underlying person may be dependent on a host of factors(biological and
others), hence for data collection, the stamina recording for the selected sample of 50 people

would be carried out before and after the new exercise regime has been carried out for a
month(Taylor & Cihon, 2017).
 The research question is “Is there any significant increase in the stamina after introduction of
the new exercise regime?”
 Considering that the sample remains the same before and after the exercise regime, hence the
paired t test would be suitable especially considering that the population standard deviation is
unknown for the samples.
STUDY 4
 This hypothetical study would aim to determine whether keto diet leads to weight reduction
or not.
 There are essentially two key variables for the given study i.e. weight before and after the
keto diet.
 The weight for the respondents before and after the prescribed diet would be measured at an
interval of two months.
 The research question is “Is there any decrease in the weight by adhering to the keto diet?”
 Considering that the sample remains the same before and after the keto diet, hence the paired
t test would be suitable especially considering that the population standard deviation is
unknown for the samples.
STUDY 5
 This hypothetical study would aim to determine whether the new exercise regime helps
people to lose weight or not.
 There are essentially two key variables for the given study i.e. weight before and after the
keto diet.
 The weight for the respondents before and after the prescribed exercise regime would be
measured at an interval of one month.
 The research question is “Is there any decrease in the weight by adhering to the prescribed
exercise regime?”
 Considering that the sample remains the same before and after the exercise regime, hence the
paired t test would be suitable especially considering that the population standard deviation is
unknown for the samples.
Correlation

Study 1
 The hypothetical study would aim to outline if there is any association between % population
(above age of 18 years) with atleast 12 years of formal education and GDP per capita.
 The key variables for the given study would be namely two i.e. the population percentage
with the required number of formal education years and GDP per capita.
 The relevant data for the selected sample of 50 nations would be obtained from IMF and
World Bank websites which provide reliable data.
 The underlying research question is “Is there any significant linear association between the
percentage of population (above age of 18 years) with atleast 12 years of formal education
and GDP per capita?”
 Both the requisite variables are numerical in nature and the significance of the linear
association between the variables can be ascertained based on the correlation analysis (Koch,
2013).
Study 2
 The hypothetical study would aim to outline if there is any linear association between hours
of study during the month before the exam and the exam score.
 The key variables for the given study would be namely two i.e. the hours of study over one
month just before the exam and the score obtained in exam.
 The relevant data would be obtained through a questionnaire which can be given to the
selected sample of 50 students.
 The underlying research question is “Is there any significant linear association between the
study hours and the score obtained in the exam?”
 Both the requisite variables are numerical in nature and the significance of the linear
association between the variables can be ascertained based on the correlation analysis.
Study 3
 The hypothetical study would aim to outline if there is any linear association between mean
weekly hours of exercise and BMI of people living in a particular city.
 The key variables for the given study would be namely two i.e. mean hours devoted to
exercise during a week and the BMI of the underlying respondent.
 The relevant data would be obtained through a survey where the exercise data can be
obtained and also the BMI for the respondent is measured (Hillier,2016).
 The underlying research question is “Is there any significant linear association between the
mean weekly hours of exercise and BMI?”
 Both the requisite variables are numerical in nature and the significance of the linear
association between the variables can be ascertained based on the correlation analysis.
Study 4

 The hypothetical study would aim to outline if there is any linear association between salary
and job satisfaction for employees in a given organization.
 The key variables for the given study would be namely two i.e. salary levels and job
satisfaction level (captured using scale from 1 to 10).
 The relevant data would be obtained through a survey where the selected sample respondent
data regarding current salary and job satisfaction level would be recorded.
 The underlying research question is “Is there any significant linear association between the
salary level and job satisfaction levels?”
 Both the requisite variables are numerical in nature and the significance of the linear
association between the variables can be ascertained based on the correlation analysis.
Study 5
 The hypothetical study would aim to outline if there is any linear association between years
of education and salary levels for a given organization.
 The key variables for the given study would be namely two i.e. years of education of the
sample employees along with their current salary level.
 The relevant data would be obtained through a survey whereby sample respondents would be
selected from the company’s employees and information about years of education and salary
would be recorded (Hastie, Tibshirani & Friedman, 2016).
 The underlying research question is “Is there any significant linear association between the
mean years of education and salary level for the selected organization?
 Both the requisite variables are numerical in nature and the significance of the linear
association between the variables can be ascertained based on the correlation analysis.
Regression

STUDY 1
 The objective of the given study is to determine the impact the number of years of work
experience on the salary levels at a selected organization.
 The independent variable would be years of work while the dependent variable would be
salary levels.
 In order to obtain the requisite data, a survey would be conducted amongst the selected
sample employee and the information about the above variables would be collected.
 The research question is “Is there any statistically significant linear relationship between the
years of work experience and employee salary at the selected organization?”
 A linear regression model would be obtained for the numerical variables. Further, the slope
would be checked for significance which would determine if the linear relationship between
the variables is significant or not (Lieberman, Nag, Hille &Basu, 2013).
STUDY 2
 The objective of the given study is to determine the impact of weekly income on the
expenditure for people in a particular city.
 The independent variable would be weekly income while the dependent variable would be
expenditure levels.
 In order to obtain the requisite data, a survey would be conducted amongst the selected
sample participants and the information about the above variables would be collected.
 The research question is “Is there any statistically significant linear relationship between the
weekly income and expenditure for people in the given city?”
 A linear regression model would be obtained for the given numerical variables. Further, the
slope would be checked for significance which would determine if the linear relationship
between the variables is significant or not.
STUDY 3
 The objective of the given study is to determine the impact of the contingent size on the
number of medals that a country wins at Olympics.
 The independent variable would be contingent size while the dependent variable would be
number of medals won at the Olympics.
 In order to obtain the requisite data, the requisite information about the selected nations
should be collected based on the online resources.
 The research question is “Is there any statistically significant linear relationship between the
contingent size and the number of medals won at the Olympics?”
 A linear regression model would be obtained for the given numerical variables. Further, the
slope would be checked for significance which would determine if the linear relationship
between the variables is significant or not.
STUDY 4

 The objective of the given study is to determine the impact of IQ on the salary level of
employees working in a given organization.
 The independent variable would be the IQ level while the dependent variable would be
current salary level.
 In order to obtain the requisite data, the selected employees would have to give Mensa IQ
test for reliable measurement of IQ while their salary can be obtained based on survey
(Medhi, 2015).
 The research question is “Is there any statistically significant linear relationship between IQ
score and current salary level of employees in a given organization?”
 A linear regression model would be obtained for the given numerical variables. Further, the
slope would be checked for significance which would determine if the linear relationship
between the variables is significant or not.
STUDY 5
 The objective of the given study is to determine the impact of number of registered cars on
the amount of car accidents annually.
 The independent variable would be registered cars while the dependent variable would be car
accidents count annually.
 In order to obtain the requisite data for selected nations online search of official websites
would be conducted.
 The research question is “Is there any statistically significant linear relationship between the
number of registered cars and number of car accidents annually?”
 A linear regression model would be obtained for the given numerical variables. Further, the
slope would be checked for significance which would determine if the linear relationship
between the variables is significant or not.
Chi-Square Analysis
STUDY 1
 The objective of this hypothetical study is to understand whether there is any relationship
between childhood sexual abuse and adolescent crimes.

 The requisite data would comprise of nominal data pertaining to two variables namely sexual
abuse in childhood and the commitment of crime in adolescence. The nature of the data
collected would be categorical as the respective replies would be in the form of “Yes” and
“No” for each of the two variables.
 In order to obtain the requisite data for the studies, those convicts who be in judicial custody
or parole and aged 25-35 years would be considered. Once the underlying sample subjects
would be identified, information about any history of sexual abuse during childhood and
crime during adolescence would be obtained by existing records and contact with the convict
if required (Taylor & Cihon, 2017).
 The research question is “Is the occurrence of sexual abuse during childhood and committing
of crime during adolescence independent of each other?”
 The requisite test to be deployed is chi-square test of independence with chi-square being the
test statistic of choice. This is the requisite test considering that both the variables are
categorical (i.e. non-numerical) in nature (Hillier, 2016).
STUDY 2
 The objective of this hypothetical study is to understand if there is a dependency relation
between gender and marital status for a given community.
 The requisite data would comprise of nominal data pertaining to two variables namely gender
and marital status of the selected respondents.
 In order to obtain the requisite data for the study, suitable sample would be obtained from the
selected community and through a survey, gender and marital status would be recorded.
 The research question is “Are gender and marital status for the selected community
independent of each other?”
 The requisite test to be deployed is chi-square test of independence with chi-square being the
test statistic of choice. This is the requisite test considering that both the variables are
categorical (i.e. non-numerical) in nature.
STUDY 3
 The objective of this hypothetical study is to understand if there is a dependency relation
between a SAT score in excess of 1550 and admission into IVY league college.
 The requisite data would comprise of nominal data pertaining to two variables namely the
SAT score and status with regards to admission in IVY league college for the selected
respondents.
 In order to obtain the requisite data for the study, suitable sample would be obtained and then
based on survey the relevant information would be collected about the variables of interest.
 The research question is “Are SAT score in excess of 1,550 and admission in IVY league
college independent of each other?”

 The requisite test to be deployed is chi-square test of independence with chi-square being the
test statistic of choice. This is the requisite test considering that both the variables are
categorical (i.e. non-numerical) in nature.
STUDY 4
 The objective of this hypothetical study is to understand if there is a dependency relation
between any of the parents suffering from diabetes and the children suffering from diabetes.
 The requisite data would comprise of nominal data pertaining to two variables namely the
status of parents and concerned child with regards to diabetes.
 In order to obtain the requisite data for the study, suitable sample would be obtained and
status about diabetes for the subject and parents would be obtained through a survey.
 The research question is “Is incidence of diabetes in either of the parents and child
independent of each other?”
 The requisite test to be deployed is chi-square test of independence with chi-square being the
test statistic of choice. This is the requisite test considering that both the variables are
categorical (i.e. non-numerical) in nature.
STUDY 5
 The objective of this hypothetical study is to understand if there is a dependency relation
between smoking and incidence of lung cancer.
 The requisite data would comprise of nominal data pertaining to two variables namely if the
subject smokes or not and whether he/she is a lung cancer patient.
 In order to obtain the requisite data for the study, suitable sample would be obtained from
lung cancer hospital and through survey of selected visitors, the requisite information would
be obtained (Flick, 2015).
 The research question is “Is there any relationship between smoking and incidence of lung
cancer?”
 The requisite test to be deployed is chi-square test of independence with chi-square being the
test statistic of choice. This is the requisite test considering that both the variables are
categorical (i.e. non-numerical) in nature.
References
Eriksson, P. & Kovalainen, A. (2015). Quantitative methods in business research (3rded.).
London: Sage Publications.

Fehr, F. H., & Grossman, G. (2013).An introduction to sets, probability and hypothesis testing
(3rded.). Ohio: Heath.
Flick, U. (2015). Introducing research methodology: A beginner's guide to doing a research
project (4thed.). New York: Sage Publications.
Hastie, T., Tibshirani, R. & Friedman, J. (2016). The Elements of Statistical Learning
(4thed.). New York: Springer Publications.
Hillier, F. (2016).Introduction to Operations Research.(6thed.). New York: McGraw Hill
Publications.
Koch, K.R. (2013). Parameter Estimation and Hypothesis Testing in Linear Models (2nded.).
London: Springer Science & Business Media.
Lieberman, F. J., Nag, B., Hiller, F.S. &Basu, P. (2013).Introduction To Operations Research
(5thed.).New Delhi: Tata McGraw Hill Publishers.
Lind, A.D., Marchal, G.W. &Wathen, A.S. (2015).Statistical Techniques in Business and
Economics (15thed.). New York : McGraw-Hill/Irwin.
Medhi, J. (2015). Statistical Methods: An Introductory Text (4thed.). Sydney: New Age
International.
Taylor, K. J. & Cihon, C. (2017).Statistical Techniques for Data Analysis (2nded.). Melbourne:
CRC Press.