# 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”?

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

LIVING ADDED

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%)”

https://www.nccih.nih.gov/research/research-results/national-survey-reveals-increased-useof-yoga-meditation-and-chiropractic-care-among-us-adults

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…

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