# Statistics Question

I am assigned the project alone so there is no group.

## Math 54 – Hypothesis Testing Project

There are many claims that are made which are suspect. Have you ever wondered if really “four out of five dentists surveyed recommend Crest toothpaste” or if “people prefer Pepsi over Coke”?

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Your task is to perform some real-world inferential statistics. Try to come up with something of interest to you instead of some contrived situation. The project will involve forming a hypothesis, then collecting the data necessary to conduct the test of the hypothesis, organizing the data, and finally analyzing and interpreting the results.

Project Timeline

Form a group and submit a proposal.

This is a group project with a maximum of 3 students in a group.  So a group of 2 or 3 students can be formed.  You can post a message in the “Project Q&A” discussion forum to find someone in class to work with you.

You need to submit a proposal defining what it is that you wish to test, and how you wish to go about testing it (think back to the types of sampling). E-mail me your proposal from the Canvas Inbox by Friday, February 3, 2023, 9 am EST. Be sure to define the population being studied clearly (Santa Monica College Students, People in Los Angeles County, People driving a car, etc).

Make sure you get the project cleared with me before you go collect the data. One person wanted to telephone survey some people and was talking in the range of spending a hundred dollars on a phone bill if she called everyone she said she was going to. The project should not cost you very much money to implement. It will take some time, however, and you should not wait until it’s almost due to get started on it.

What can you test?

Some things are easier to test than other things. The purpose of this project is to expose you to the process of hypothesis testing with a real-world application. You may test means, proportions, standard deviations, or linear correlations. Come up with a claim that you have heard or that interests you.

I have attached a couple of examples of students’ projects in previous semesters.

Work on your project and post it in the “Project Presentations” Forum (Due: Wednesday Feb 8,2023.)

The project report will include:

1) A description of the problem, and why you think it is important, or what you hope to gain from testing the hypot h esis.

2) Explanation of how you collected your data and what method of sampling you used. It should also include all data collected.

3) Hypotheses (H0 and H1).

4) Statistical formulas used to perform the hypothesis test (you may write the formulas by hand), tables, graphs and values. Show work on how you calculated your test statistic and the P-value.

5) Requirement check for the test.

6) A decision and conclusion should be stated. An analysis should follow with what the conclusion means in terms of the original problem.

7) The report must be typed up in a ppt or pdf.

Your project must be posted in the “Project Presentations” Forum. As part of your project grade, you must read at least 1 project presentation and post your comments.

Claim
Stop At the Stop Sign
In a Venice neighborhood, residents have
been complaining about the lack of stopping
at stop signs. They claim that men fail to stop
more than women do.
Population: Drivers in
Venice
MARISSA & MAKAILA
Collecting Data
Location Facts

Sat at the corner of Penmar Avenue and Appleton (partially hidden)
between 2:30pm to 3:45pm on a Friday

Every other car was recorded (systematic sampling):
 Male or Female
*Located 1/5 of a mile
from a park
 Stop or Did not stop
*Stopped was considered slowing down
to the point of almost stopping or
completely stopping
P-hat (m) = x/n =
Data
Stopped
Did Not Stop
Male
40
37
Female
25
33
x(m) = 37
n(m) = 77
*3/10 of a mile from an
elementary school
(Male)
37/77 =
0.4805
P-hat (f) = x/n
48.05%
(Female)
=
33/58
48.05%
(Failed)
=
0.5690
56.9%
56.9%
(Failed))
x(f) = 33
n(f) = 58
Significance level= 0.05
51.95%
(succeeded)
43.1%
(succeeded)
1
Hypothesis Test
Step #2
Requirements (Satisfied)
Step #1
(1) The sample was independently obtained using simple random
sample
Null Hypothesis
P(m) = P(f)
The proportion of males that fail to stop
is the same as the proportion of females
that fail to stop
Alternative Hypothesis
P(m) > P(f)
The proportion of males that fail to stop
is greater than the proportion of females
that fail to stop
(2) n(m)< 5% of N(m) & n(f) 10 n(f) x p(f) x (1 – p(f)) > 10
(77) x (.4805) x (1 – .4805) > 10
(58) x (.244) x (1 – .244)> 10
(36.9985) x (.5195) > 10
(14.15) x (.756) > 10
19.22 > 10
10.70 > 10
Right Tail Test
Test Statistic
0.4805 – 0.5690
Step #3
.
√.5185(.4815) √(1/77) + (1/58)
=
– .0885
.
(.4997)(.1739)
P-value = .8457
= -1.018
Step #
Decision 4
*Reject if P value is < alpha Otherwise do not reject P-value = .8457 > alpha = .05
Step #5
Conclusion
There is not sufficient evidence to conclude that
men fail to stop more often than females do.
Do Not Reject the Null Hypothesis
2
Interesting Observation
There were only a total of 4
complete stops in the 135 cars
recorded
3
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Yoga and Meditation
During Quarantine
FEELING
STRESSED?
HAS
QUARANTINED
ON TO THAT?
A common practice for stress
management has been adopted by
many in the form of yoga and
meditation.
A survey was conducted in
2016 by Yoga Journal as well
as Yoga Alliance.
Survey data for this comprehensive study of the consumer yoga market was
collected by Ipsos Public Affairs on behalf of Yoga Journal and Yoga Alliance.
The results indicate that women represent 72 percent of US practitioners, with
men and older Americans doing Downward Dog at a growing rate. Thirty-four
percent of Americans, or 80 million people, say they are likely to try yoga for the
ﬁrst time in the next 12 months.
https://www.prnewswire.com/news-releases/2016-yoga-in-america-study-conducted-by-yo
ga-journal-and-yoga-alliance-reveals-growth-and-benefits-of-the-practice-300203418.html
36.7 million out of
323.1 million
Americans, in
2016, practiced
yoga regularly.
That equated to
11% of the
American
population in 2016!
According to the Statistics From the National Health
Interview Survey
“Yoga was the most commonly used complementary
health approach among U.S. adults in 2012 (9.5%) and
2017 (14.3%)”
We believe that a higher proportion of
California residents have taken up
yoga or meditation in order to manage
the stress of quarantined living.
So we set out to test
this theory…
The goal was to ﬁgure out if the
percentage of California residents
practicing yoga or meditation to help
deal with their anxiety/stress during
the Covid-19 pandemic was over 14.3%.
We achieved this by using a survey
website as well as a phone application
that helped us reach out to random
residents so that they could answer
the question at hand.
We hypothesized that over 14.3% of the
California population have taken up
meditation or yoga as a way to
manage stress during the pandemic.
This is done with 95% conﬁdence.
Testing our hypothesis with a signiﬁcance level of 0.05, we
randomly surveyed 82 residents of California and let the
results of the survey be representative of the total population.
Our overall goal is to try and prove that the majority of the
population in California practice yoga or meditation as a form
of stress management during the lockdown caused by the
COVID-19 pandemic.
Yoga, as well as meditation, have moved to the forefront of
healthy living practices. The beneﬁts of yoga/meditation can
stretch from a person’s physical well being to their mental health
as well. Because of COVID, many online yoga and meditation
tools became available to the people as a way to manage their
anxiety and/or stress. The COVID-19 pandemic has been
challenging, and a lot of different emotions, that may cause
stress, have become present during this time.
We utilized the website surveyplanet.com as well as the Nextdoor
app as ways to reach out, speciﬁcally to California residents.
Each individual was asked if they had practiced any form of yoga
or meditation as a type of stress management for their mental
health during their time in quarantine.
+
After receiving a simple random sample of
answers, we analyzed and interpreted the
data in order to ﬁnd out if our hypothesis was
correct…
TO OUR SURPRISE,
The results showed that 36, of the 82 people
who took the survey, used yoga/meditation as
tools to manage their emotions.
Our Hypothesis…
Hypothesis thesis
Ho: p = 0.143 (null)
H1: p > 0.143 (alternative)
Right-tailed Test (P-value approach)
Level of signiﬁcance: 0.05%
Requirements for Hypothesis Testing
1- Simple random sample
n= 82, p= .143, p̂= .439
2- np(1-p) greater than or equal to 10
82 x .143(1 – .143)=10.049
3- The sample is independent
n is less than or equal to 0.05N
Test statistic of the population proportion
Using the calculator TI-84 we found:
(test statistic) z = 7.657
P-value = 0.000
If the p-value is less than the level of signiﬁcance than we reject the null
hypothesis.
Because the P-value=.000 was less than .05, we reject the null hypothesis. There
is suﬃcient evidence to prove our hypothesis correct. The proportion of
California residents who practice yoga during quarantine is over 14.3%.
While surprising, we’re glad that a large
majority of residents have taken their mental
health into consideration by learning to
meditate or perform yoga.
The results speak for themselves…
We believe that the more people should consider
taking up these practices, because a calm body
and mind can help you get through these tough
times…

What Are the Benefits of Doing a Yoga Practice?

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