Name: Jeet Rupani
Objectives
The purpose of this project is to give students experience in collecting discrete and
continuous data and determining 2-sided confidence intervals. This Mini-Project will
require that
(i) discrete and continuous data be collected
(ii) confidence intervals on the population mean and population standard deviation be
determined
WE HAVE TO
1. Collect (through surveys or interviews) or find online between 10 and 20 observations
from discrete data of your choice that is NOT video game related, number of siblings,
number of cups of coffee (or any other beverage), number of credit hours, shoe size
2. Compute the sample mean and sample standard deviation of the observations from
your discrete data.
3. For the discrete data, create a 90% 2-sided confidence interval on the population
mean. Do not use Eq. 8.11 in the text. We will know that you use AI or copied
something from the internet.
4. For the discrete data, create a 90% 2-sided confidence interval on the population
standard deviation.
5. Collect or find between 10 and 20 observations from continuous data that is NOT
video game related, distance someone lives from campus, GPA, any sports data about
a team or player
6. Compute the sample mean and sample standard deviation of the observations from
the continuous data.
7. For the continuous data, create a 90% 2-sided confidence interval on the population
mean. Do not use
Eq. 8.11 in the text. We will know that you use AI or copied something from the internet.
8. For the continuous data, create a 90% 2-sided confidence interval on the population
standard deviation.
9. Write up your findings using the template provided in the last pages of this document.
10. Upload your report as a Word doc or docx (no pdfs permitted) to the Mini-Project
Upload in the Mini- Project module on Canvas before 11:59 pm AZ time Monday,
4/20/26.
Discrete Data Description
Describe the discrete data you collected, how many observations you took, and
how you collected the observations (generated, collected on the internet, how?).
If websites were used, include URLs and titles.
The discrete data collected for this project consists of the amount of money (in dollars $)
an individual pays to get a haircut. I went around campus and asked a total of 15
separate people to answer my question (15 observations obtained).
Discrete Data Table
Show the raw discrete data here, in a table. Include units and any other necessary
descriptors. Have a sentence before the data is presented. Example: “The data
collected for this project may be seen in the following table:”
The data collected for this project for discrete data is based on how much an individual
pays for a haircut in dollars and has been displayed in the following table.
DISCRETE DATA
NO.
AMOUNT PAID BY AN INDIVIDUAL FOR A HAIRCUT
(DOLLARS $)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
40
28
37
15
45
28
45
15
15
15
37
40
15
37
28
Discrete Data Confidence Intervals
For the discrete data, show the equations you used for the upper and lower
bounds of the confidence intervals on the (a) population mean and (b) population
standard deviation. Use the equation editor. Clearly state the upper and lower
bound values and remember to include the units.
Calculating the Sample Mean (𝑥)
n=15
𝑥=
40+28+37+15+45+28+45+15+15+15+15+37+40+15+37+28
15
2
Σ(𝑥𝑖 −𝑥 )
Sample standard deviation (s) = √
𝑛−1
= $29.33
1927.35
= √
14
= $11.73
(a)
Lower Bound:
𝑠
11.73
√
√15
𝑥 − 𝑡𝛼,𝑛−1 ⋅ 𝑛 = 29.33 − 1.761 ⋅
2
= $24.00
Upper Bound:
𝑠
11.73
√
√15
𝑥 + 𝑡𝛼,𝑛−1 ⋅ 𝑛 = 29.33 + 1.761 ⋅
2
= $34.06
Hence our 90% 2 sided confidence interval on the population mean is $24 ≤ 𝜇 ≤
$34.06.
(b)
Lower Bound:
(𝑛−1)𝑠2
√ 𝜘𝛼2
2
,𝑛−1
14⋅137.67
1927.35
= √ 23.685 = √ 23.685 = √81.35 = $9.02
Upper Bound:
(𝑛−1)𝑠2
2
√𝜘1−𝛼
2
,𝑛−1
14⋅137.67
= √
6.571
1927.35
= √ 6.571 = √293.22 = $17.12
Hence our 90% two sided confidence interval on the population standard deviation is
$9.02 ≤ 𝜎 ≤ $17.12.
Continuous Data Description
Describe the continuous data you collected, how many observations you took,
and how you collected the observations (generated, collected on the internet,
how?). If websites were used, include URLs and titles.
The continuous data collected for this project consists of the daily highest recorded
temperatures over the last 15 days in degrees Fahrenheit. I used my phone's weather
app to gather the required data (15 observations).
Continuous Data Table
Show the raw continuous data here, in a table. Include units and any other
necessary descriptors. Have a sentence before the data is presented. Example:
“The data collected for this project may be seen in the following table:”
The data collected for this project for continuous data is based on the highest
temperature recorded every day over the last 15 days in degrees Fahrenheit and has
been displayed in the following table.
CONTINUOUS DATA
NO.
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
HIGHEST TEMPERATURE IN TEMPE OVER THE LAST 15 DAYS
(° FAHRENHEIT)
89
92
78
91
95
94
90
88
80
80
77
85
87
83
90
Continuous Data Confidence Intervals
For the continuous data, show the equations you used for the upper and lower
bounds of the confidence interval on (a) the population mean and (b) the
population standard deviation. Use the equation editor. Clearly state the upper
and lower bound values and remember to include the units.
n=15
First we calculate the Sample Mean
𝑥=
89+92+78+91+95+94+90+88+80+80+77+85+87+83+90
15
= 86.60°F
Calculating sample standard deviation
2
Σ(𝑥𝑖 −𝑥 )
473.60
s=√
= √
= 5.82°F
𝑛−1
14
(a)
Lower Bound:
𝑠
5.82
√
√15
𝑥 − 𝑡𝛼,𝑛−1 ⋅ 𝑛 = 86.60 − 1.761 ⋅
2
= 86.60 − 2.65 = 83.95°F
Upper Bound:
𝑠
5.82
√
√15
𝑥 + 𝑡𝛼,𝑛−1 ⋅ 𝑛 = 86.60 + 1.761 ⋅
2
= 86.60 + 2.65 = 89.25°F
Hence the 90% two sided confidence interval on the population mean is
83.95°F ≤ 𝜇 ≤ 89.25°F.
(b)
Lower Bound:
(𝑛−1)𝑠2
√ 𝜘𝛼2
2
14⋅(5.82)2
= √
23.685
,𝑛−1
473.62
= √
23.685
= √19.99 = 4.47°F
Upper Bound:
(𝑛−1)𝑠2
2
√𝜘1−𝛼
2
,𝑛−1
14⋅(5.82)2
= √
6.571
473.62
= √ 6.571 = √72.08 = 8.49°F
Hence the 90% two sided confidence interval on the population standard deviation is
4.47°F ≤ 𝜎 ≤ 8.49°F.
References
Google LLC. (2026). Google Weather [Mobile app]. Google Play Store.
https://play.google.com/store/apps