final stage stats #2

8/3/2019 Final Stage Stats #2

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Style for Research Reports in Statistics

Introduction to Stat 1510 Research Project


Arty Sanchez

Taft College


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Abstract

The statistical analysis of our sample surveys shows us that there are many different opinions

and outcomes that come with different people taking a survey. Bar Graphs and Box and whisker

plots were used to illustrate the shapes and to compare the data between the different results of

the sample size of the surveys. The results obtained from the analysis were used to discuss the

datas sample size surveys results.

Introduction

We use statistics a lot in todays century to have a better understanding on different events and

situations. We use statistics to help us with political data and also for data regarding any

information where people are trying to find the statistics of their certain outcomes. The survey

samples are used to create an understanding of the population to help researchers have a better

understanding by creating an analysis of the data collected. The data will be examined to show

the differences and similarities between each survey taken.

Method

Participants

The participants that took place in these surveys were given a survey by students of Mr. Brian

Jeans classroom. Each student was required to have random people fill out each survey fully to

where every answer was filled in. After the student had all ten of their surveys filled out, they


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were required to enter the data on a website were all the data would be collected and recorded for

the use of this project for each student, that way there would be a big enough sample size for

each student to work with.

Materials

Each person that took a survey had the same questions given to them. The people who took the

surveys can be described as materials because they were the main material which helped us

collect our data. The use of the internet was helpful in retrieving the population sample data for

the survey. Also the use of the calculator to help create graphs, solve problems, and to help find

my sample size of 60 surveys by using the calculators random integer key to get each survey

randomly.

Procedures

The first step was collecting each surveys data randomly by creating a sample size of 60 surveys

by using the calculators random integer key, randInt. This gave me my 60 random sample survey

numbers, that way I only use those surveys data only for my project. After having my sample

surveys, I went ahead and starting collecting data from sample surveys of how many males took

the survey and how many females took the survey and created a bar graph that shows the

difference between the two. Also I created a box and whisker plot by collecting the data of male

and females certain hours that they work per week. The same procedures were done with finding

the results for the Health Care Bill being passed and whether or not people think President


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Obama will be reelected for president again. All it took was a little time, patience, and correct

data to be recorded.

Results

Bar Graph for Obama to be reelected


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The results for this bar graph show that the females have a bigger sample size then the men, but

the females are more in favor of President Obama not to be reelected. The males are also more in

favor of Obama not being reelected. This shows how similarities between the males and females

towards this question of the survey.

Bar Graph for Gender


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The bar graph shown above shows the difference between how many males took the survey and

how many females took the survey regarding to my sample size. It shows that twenty-three males

and thirty-seven females have taken the survey out of a random sample size of sixty.

Box and Whisker Plot for (Hours of Work Per. Week)

Male n= 23 =31.6086 minX=0 Q1=20 med.=40 Q3=47 maxX=65

Female n= 37 =24.8108 minX=0 Q1=0 med=32 Q3=40 maxX=60


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The box and whisker blot shown above shows that males have a greater percentage of working

more hours than females do. The females second whisker is not there because minx and Q1 are

both zero. The males did have a smaller sample size with a lot of working hours, but the women

had a lot of zeros on hours worked per week for their sample size creating their box and whisker

plot to be on lower amount of hours worked side of the graph.

Bar Graph for Results on Health Care Bill


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In the bar graph shown above the males seem to be leaning more towards the undecided answer

for whether or not they agree with the health care bill being passed. The Females also seem to be

leaning for towards the undecided answer as well. In second for the females is No on the Health

Care Bill being passed, women do not agree with it. And in second place for the males the men

are barely above with No as well on the Health Care Bill being passed.

Results

The results of the statistical analysis showed us that there are many different opinions and

outcomes that come with different people taking a survey. The box and whisker plot

demonstrated a significant difference in male and females hours worked per week with this

sample size. The same goes for the bar graphs of results on health care bill, the bar graph for

Obama to be reelected, and the bar graph for gender. Each survey in the sample size had

different results. This shows the many different results and answers people agree upon with

certain questions relating to our current events.

Discussion

# 1: I decided to use a scatter plot to see if there was a relationship between height and weight;

the graph was linear so I chose Pearsons correlation. This concludes that there is a positive

correlation between a persons height and weight.


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The same goes for ring and shoe size. I decided to use a scatter plot to see if there was a

relationship between the two; the graph was linear so I chose Pearsons correlation. This

concludes that there is a positive correlation between a persons ring and shoe size.

# 2: I decided to use the Wilcoxon Rank-Sum Test. This test fails to reject the null hypothesis,

which suggests that there is not enough evidence to suggest a difference in Annual Gross Income

based on gender between men and women.

# 3: I decided to use the CHI-Squared Test of Independence for all three parts of this question.

The P-value is greater than alpha on all three parts of this question, which rejected the Null

Hypothesis which shows

# 4: I decided to use an odds ratio test since I only had one ambidextrous person in my sample,

so my results turned out to be FTR, There is not enough evidence to suggest there is a correlation

between handedness and those in favor of the death penalty.

#5 I decided to use the CHI-Squared Test of Independence for my question, which was is there a

relationship between people in favor of the death penalty and people who believe President

Obama to be re-elected? In my analysis the p-value was greater than alpha, so it rejects the null

hypothesis, which suggests that there is a relationship between the two.

#6 I decided to use the Kruskal-Wallis Test for this question. I had four lists from my sample

size for different ethnicities and how much their annual income is. Out of my sample size of 60 I

seemed to have more white people than any other ethnicity. So most likely they would be the

ethnicity that makes a greater annual income. And my p-value was greater than alpha so it rejects


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the Null hypothesis suggesting that there is enough evidence that a certain ethnicity from my

sample size makes a higher Annual Income than the other ethnicities.

Appendix

My Sample Size throughout each question is 60.

1. Is there a relationship between an appropriate combination of a persons height,weight, ring or shoe size?

Scatter Plot betweenpersons Height and Weight

Pearsons Correlation

Ho: p=0Ha: p>0

r= .5325

P-value= 5.9505E-6

P-value = 0.0000Alpha=0.05

Rejects the Null hypothesis, there is not enough information to suggest that there is a positivecorrelation between Height and Weight. With a 95% confidence interval the correlation

coefficient is between (0.2731, 0.7143).


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Scatter Plot for Ring and Shoe Size

Pearsons Correlation

Ho: p=0Ha: p>0

r= .7894

P-value= 3.3089E-7P-value = 0.0000

Alpha=0.05

Rejects the Null hypothesis, there is not enough information to suggest that there is a positivecorrelation between Ring and Shoe size. With a 95% confidence interval the correlation

coefficient is between (0.4928, 0.8462).

2. Is there a difference in gross income based on gender?

Wilcox Rank-Sum

Ho: Theta male gross income-Theta female gross income=0

Ha: Theta male gross income-Theta female gross income does not =0

T= .8798

P-value= .3825

Fails to reject the null hypothesis, there is enough evidence to suggest that there is a differencebetween males and females gross income.


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3. Is there a relationship between political party anda) if the respondent feels president Obama will be re-elected?

Satisfies the properties of a multinomial experiment, count data, all expected values are greaterthan 1, No more than 20% of the expected values are < 5.

Ho: Political Affiliation and the respondent feeling President Obama will be re-elected areIndependent

Ha: Political Affiliation and the respondent feeling President Obama will be re-elected are

Dependent

The numbers in the picture follow the table below:

Yes No UndecidedOther

Republican

IndependentDemocrat

xSquared= 8.3152P-value= .2159

df=6

Alpha =0.05

CHI-Squared Test of Independence expected values: Violation if more that 20% are < 5.

1.6666, 1.5333, .8

10.8333, 9.9666, 5.27.0833, 6.5166, 3.4

5.4166, 4.9833, 2.6

Rejects the Null hypothesis, there is enough evidence to suggest that there is a relationship

between Political parties and the respondents that feel President Obama will be re-elected.


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b) if the respondent is in favor of the health care bill a passed?Ho: Political Party and Health Care Bill Independent

Ha: Political Party and Health Care Bill Dependent

Satisfies the properties of a multinomial experiment, count data, all expected values are greater

than 1, No more than 20% of the expected values are < 5.


Yes No UndecidedOther

Republican

IndependentDemocrat

xSquared= 11.4411

P-value= .0756

df= 6Alpha= 0.05


2.7, 3.45, 2.85

7.5, 9.5833, 7.9166

4.8, 6.1333, 5.06663, 3.8333, 3.1666


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Rejects the Null hypothesis, there is enough evidence to suggest that there is a relationship

between political party and respondents in favor of the health care bill as passed.

c) if the respondent is in favor of the death penalty?Ho: Political Party Affiliation and respondents in favor of the death penalty are Independent.

Ha: Political Party Affiliation and respondents in favor of the death penalty are Dependent.


Yes No Undecided

OtherRepublican

Independent

Democrat

xSquared= 4.8095

P-Value= .5684df= 6


5, 2.8333, 2.1666

14.5, 8.2166, 6.2833

6, 3.4, 2.64.5, 2.55, 1.95

Rejects the Null hypothesis, there is enough evidence to suggest that there is a relationshipbetween political party and the respondents in favor of the death penalty.


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4. Is there a relationship between handedness andOdds Ratio Test

a) in favor of the death penalty?Ho: There is a relationship between handedness and death penalty.

Ha: There is not a relationship between handedness and death penalty.

Alpha = 0.05

P-value 0.7924

Fails to reject the Null hypothesis, there is not enough evidence to suggest that there is arelationship between handedness and those in favor of the death penalty.

b) amount of water consumed?

Histogram shows that more water is consumed by right handed people than left handed people. I

had 3 left handed people and 1 ambidextrous person, and data wasnt able to be compared.

Ho: Different handedness people drink the same amount of water.

Ha: At least one handedness drinks more water than the other.

Alpha=0.05

P-value= .6096


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Rejects the Null hypothesis, there is enough evidence to suggest that right hand people drink

more water than left handed people.

5. Is there a relationship between people who believe in the death penalty and peoplewho believe that President Obama will be re-elected?

Ho: People who believe in the death penalty and those who believe President Obama will be re-elected are Independent

Ha: People who believe in the death penalty and those who believe President Obama will be re-

elected are Dependent


Yes Obama Reelected No Obama Reelected Undecided Obama ReelectedYes for Death PenaltyNo for Death Penalty

Undecided for Death Penalty

Alpha= 0.05

xSquared= 4.1189

P-value= .3901df= 4

CHI-Squared Test of Independence expected values: Violation if more that 20% are < 5

7.5833, 3.6833, 1.7333

15.75, 7.65, 3.6

11.6666, 5.6666, 2.6666


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Rejects the Null hypothesis, there enough evidence to suggest that there are similarities between

people who believe in the death penalty and people who believe that President Obama will be re-

elected.

6. Is there a certain ethnicity from my sample size that makes a higher Annual Incomethan the other ethnicities?

Kruskal-Wallis Test

Ho: Theta Hispanics=Theta Blacks=Theta Whites=Theta Other

Ha: at least one is not equal

L1:White= 37 people

L2:Balck=4 people

L3:Hispanic=16 people

L4:Other= 3 people

Alpha=0.05

P-Value= .1892Statistics, H =4.7729

Rejects the Null hypothesis, there is enough evidence to suggest that there is a certain ethnicity

from my sample size that makes a higher Annual Income than the other ethnicities.


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