Math Project

1
Math 227 Project 2 Inferences on Two Population Parameters
In this project, you will draw inferences on comparing two population parameters: proportions, means,
or standard deviations (or variances). You will describe a problem including a general claim made about
comparing two population parameters, collect data, test hypotheses, and construct and interpret a
confidence interval to determine whether the claim made about two population parameters can still be
supported by the samples collected. You will, then, write a report on your findings including all the
required components below and turn in by the stated due date according to the guidelines provided in
this paper.
Required components:
1. Understand the Problem
a) Select a parameter of your choice: proportion, mean, or standard deviation, for which a
general claim can be (or has been) made. Please try to decide on something that you are
interested in knowing about. Who (what) are the two populations you want to compare?
b) Describe the problem including a general claim made about two specific populations:
c) Identify any relevant variables to the above problem:
Are these variables categorical or numerical?
d) Collect either categorical or numerical data from two relevant samples. You must collect at
least 30 data values from each sample. Discuss how your data has been collected and whether
you were able to collect a random sample of data. If a random sampling was not possible, please
explain why not.
2. Analyze the Data
a) What parameter is being compared? _________________________
b) What is the response variable in the problem?
c) Is sampling dependent or independent?
d) Provide appropriate numerical measures and graphical displays in answering the problem.
e) Discuss whether required conditions are met to test hypotheses depending on the parameter
being addressed.
Two Population
Proportions-
Independent
(Section 11.1)
Two Population
means from
Matched-Pairs-
Dependent
(Section 11.2)
Two Population
means-
Independent
(Section 11.3)
Two Population
standard
deviation (or
variance)
(Section 11.4)
Required Conditions
for hypotheses
testing and
construction a
confidence interval

for each sample
and the sample
size is no more
than 5% of
population size &
Each sample
size is greater
than 30 or the
differences
come from a
population that
Each sample
size is greater
than 30 or each
population is
normally
distributed
The data are
normally
distributed.
ˆ ˆ(1 ) 10np p 
2
normal
distribution
is normally
distributed
normally
distributed
with no outliers
Distributions
(Test Statistic)
z-distribution Student’s t-
distribution
with n-1 degree
of freedom
Student’s t-
distribution
F-Distribution
f) Test hypotheses using
 Determine the null and alternative hypotheses. Use proper symbols.
 Use technology to find the test statistics.
 Use technology to find the P-value. Provide the meaning of the P-value about your
problem. Also, provide a list of steps in finding the P-value using StatCrunch.
 Make the decision on whether to reject the null hypothesis or not.
Provide a statement about the significance of the sample difference and determine
whether the claim made about two population parameters can still be supported by the
samples collected. Do you think the population have the same parameters and the
difference of sample statistics just happened due to sampling variability (random
chance) or do you think the sample difference is indeed significant and it suggests that
the population parameters are more likely different? Explain according to the P-value.
 State the conclusion about the claim.
g) Construct and interpret a 95% confidence interval for the difference between two population
parameters
 State the confidence interval. Also, provide a list of steps in constructing the confidence
interval using StatCrunch.
 Interpret the confidence interval about your problem.
 Does the confidence interval support the conclusion of the hypothesis testing?
3. Draw Conclusions
a) What do the results you got indicate about the inference on comparing two population
parameters? Decide whether the claim made about two population parameters can still be
supported by the samples collected. Explain using the results of the hypothesis testing and the
confidence interval.
b) If it is relevant or meaningful in context, think of a way that these results could be used in
practice.
4. Summarize
Write a short summary of the main findings that you discovered.
0.05 
3
Grades will be based on:
1. Explanation of your topic and appropriate responses in part 1 Understanding the problem
[10 pts],
2. Relevance and completeness of the analysis of the data including appropriate responses in
part 2 Analyze the paired Data [50 pts],
3. Completeness and appropriateness of drawing conclusions in part 3 Draw conclusions [20
pts],
4. Clear summary of the main findings in part 4 Summarize [10 pts], and
5. Overall quality of the report and adherence of the project guidelines [10 pts]
Submission Guidelines and the due date:
The report including all graphs and characters must be generated using computer and only digital
version will be accepted. Please combine the files into single pdf, MS word format, using any app. The
report should contain the title, your name, date, course name and instructor’s name. The report should
not contain any misspelled words. The report will not be returned to you.
The project score sheet along with the title of your project and the website where you collected or
found your data (page 4 of this guidelines), must be submitted to the instructor.
Math 227 Project 3 Inferences on Two Population Parameters-Score Sheet (Total 100 points)
4
Name:________________________________________ Date:__________________________________
Title of the project: ____________________________________________________________________
Website where you found the data:_______________________________________________________
Project Grade: __________________________________
Required Tasks Grading criteria Comments/Scores
1. Understand the Problem
a) Select a parameter of your choice: proportion, mean, or
standard deviation, for which a general claim can be
(or has been) made. Please try to decide on something
that you are interested in knowing about. Who (what)
are the two populations you want to compare?
b) Describe the problem including a general claim made
about two specific populations:
c) Identify any relevant variables to the above problem:
Are these variables categorical or numerical?
d) Collect either categorical or numerical data from
two relevant samples. You must collect at least 30
data values from each sample. Discuss how your data
has been collected and whether you were able to
collect a random sample of data. If a random sampling
was not possible, please explain why not.
1. Explanation of your
topic and appropriate
responses in step 1
Understanding the
problem [10 pts]
2. Analyze the paired Data
a) What parameter is being compared?
_________________________
b) What is the response variable in the problem?
c) Is sampling dependent or independent?
d) Provide appropriate numerical measures and graphical
displays in answering the problem.
e) Discuss whether required conditions are met to test
hypotheses depending on the parameter being
addressed.
f) Test hypotheses using
 Determine the null and alternative hypotheses. Use
proper symbols.
 Use technology to find the test statistics
 Use technology to find the P-value. Provide the
meaning of the P-value about your problem. Also,
provide a list of steps in finding the P-value using
StatCrunch.
 Make the decision on whether to reject the null
hypothesis or not.
Provide a statement about the significance of the
sample difference and determine whether the claim
made about two population parameters can still be
supported by the samples collected. Do you think
the population have the same parameters and the
difference of sample statistics just happened due to
sampling variability (random chance) or do you think
2. Relevance and
completeness of the
analysis of the data
including appropriate
responses in step 2
Analyze the paired
Data [50 pts]
0.05 
5
the sample difference is indeed significant and it
suggests that the population parameters are more
likely be different? Explain according to the P-value.
 State the conclusion about the claim.
g) Construct and interpret a 95% confidence interval for the
difference between two population parameters
 State the confidence interval. Also, provide a list of
steps in constructing the confidence interval using
StatCrunch.
 Interpret the confidence interval about your
problem.
 Does the confidence interval support the conclusion
of the hypothesis testing?
3. Draw Conclusions
a) What do the results you got indicate about the inference
on comparing two population parameters? Decide
whether the claim made about two population
parameters can still be supported by the samples
collected. Explain using the results of the hypothesis
testing and the confidence interval.
b) If it is relevant or meaningful in context, think of a way
that these results could be used in practice.
3. Completeness and
appropriateness of
drawing conclusions
in step 3 Draw
conclusions [20 pts]
4. Summarize
Write a short summary of the main findings that you
discovered.
4. Clear summary of the
main findings in step 4
Summarize [10 pts]
5. Overall quality of the report 5. Overall quality of the
report and adherence
of the project
guidelines [10 pts]

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