# 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

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