MAT 201 Saint Leo University Confidence Interval for P Analysis

Semester Project Part 4 – Confidence Interval for p
Points on Rubric: 20 Submit as a file upload
Use your data set from Part 2 of the Project and your summary statistics from Part 3, to complete
this portion of the project.
Place your results in a semi-professional looking report. Remember to include your name, date,
title, page numbers, etc.
Your goal is to use your qualitative variable with your data to create and interpret a confidence
interval for the population proportion. In order to calculate and interpret these proportions, you
will need to determine which level of your qualitative variable you would like to consider a
“success,” statistically speaking. For example, if your qualitative variable is gender, then if you
are interested in the proportion of the population that’s female, select “female” as a success. If
your qualitative variable is something like “having a tattoo or not,” then you might want to select
“having a tattoo” as a success. Please read any comments/feedback I provided on Projects Parts
1, 2, and 3, and do not repeat previous mistakes. If there were any invalid responses in your data,
you should eliminate these responses from your sample and mention that you did this in the
introduction or conclusion of your paper.
Your report will be short, but it must contain these parts: and a
Part 1: Introduction
Provide a short introduction to the project. Specifically, briefly describe
the sample, your qualitative variable (including the two levels), your population of interest, and
what you will analyze in the project. Define what p is for analysis (e.g. if you are interested in
the proportion of your population that has a tattoo, then you would want to include a statement
that says something like, “I am interested in creating a 95%(or 99%, your choice) confidence
interval for the true percentage of all SLU students who have tattoos”.
Part 2: Confidence Interval for p: State the number of students who are in each of the two
groups and the total sample size (e.g. You could state something like: “60 SLU students were
sampled. Of these, 21 had a tattoo and 39 did not.”. Find and interpret that value.
Create a 95% CI and and a 99% CI for p.
Practically interpret this confidence interval.
Part 3: Conclusion Provide a short conclusion. Your conclusion may include assumptions made,
potential problems with the analysis, what you learned, or anything else you want to say to tie
the results together neatly.
Hints: If your QL variable has more than two levels, select one of those levels as a “success” and
treat everything else as a “failure.” When interpreting the proportions, I recommend you convert
them to percent (multiply by 100% or move the decimal place two spots to the right). However,
only work with the decimal version when using the formulas. While you’ll need to round your
final answer, please do not round the sample proportion too much before using it to calculate the
margin of error (you will have substantial rounding errors). I’d recommend rounding to 4-5
decimal places while doing the calculation, but report the final answer to just 3 decimal places.
For example, you might calculate your sample proportion to be 0.215871352… When you use it
in calculations, round it to 0.21587. However, when you interpret this sample proportion, you
would write it as 21.6%.
If your confidence interval goes below 0 or above 1, that’s okay, and you should report it the way
it’s calculated. However, when you interpret the interval, you’d want to convert any negative
lower bound to “0%” and any upper bound above 1 to “100%.” For example, if I calculated my
confidence interval to be (0.825, 1.041), I would report the interval as written, but when I
interpret the interval, I would write, “…between 82.5% and 100%.”
Sample Project RESPONSE Example – Part 4 – Confidence Interval for p.
Sample Student
MAT 201-CAxxx
Instructor: Dr. Charlotte A. Smedberg
3/16/2021
Project Part 4 – CI for p
Introduction:
In this project, I used the data generated from a sample of SLU students to estimate the
proportion of all SLU students who identify themselves as female.
Results:
58 students were sampled. Of those 58 students, 37 identified themselves as female, 20 identified
themselves as male, and one did not respond to the question. The one non-response was left in
the analysis.
63.8% of the sampled SLU students identified themselves as female. This sample proportion was
used to create the 95% confidence interval for p stated below.
(0.514, 0.762)
I am 95% confident that the true percentage of all SLU students who identify themselves as
female is between 51.4% and 76.2%.
Discussion:
Based on this sample, there is evidence that over 50% of the SLU student body identify
themselves as female on this non-random sample of 58 students on the University Campus.
These results may be biased, since the sample was taken from students enrolled in a required
course which might have a higher female enrollment than some other programs at SLU. In
addition, one student did not respond to the gender question. It’s possible this student does not
identify as male or female, but, might have also just skipped the question accidentally or didn’t
want to reveal gender in the survey.
Type
Ford edge
Ford Escape
Ford Expedition
Ford Explorer
Ford fusion
Ford Mustang
Chevy Blazer
Chevy Trax
Chevy Bolt
Chevy Camaro
Chevy Corvette
Chevy Equinox
Chevy Impala
Chevy Malibu
Chevy Sonic
Chevy Spark
Chevy Suburban
Chevy Tahoe
Chevy Traverse
Audi A3
Audi A4
Audi A5
Audi A6
Audi A7
Audi A8
Audi E-Tron
Audi Q3
Audi Q5
AudiQ7
Audi Q8
Audi TT
Milages Seating
24
5
16
5
23
9
25
7
22
5
17
4
19
5
25
5
119
5
20
4
20
2
31
5
22
5
32
5
28
5
33
4
16
9
20
9
25
8
27
5
27
5
17
4
25
5
25
5
21
5
74
5
22
5
24
5
20
5
19
5
26
4
milages
seating
sample size
mean
SD
min
Q1
median
Q3
max
31
31
27.87096774 5.290322581
19.71419444 1.553352254
16
2
20
5
24
5
26.5
5
119
9
Type
Ford
Chevy
Audi
Total
Frequency
Proportion
6
0.1935
13
0.4194
12
0.3871
31
1
Frequency BarChart Type Vehicl
14
12
10
8
6
4
2
0
Ford
Chevy
y BarChart Type Vehicle
Chevy
Audi