final stage stats #2
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Introduction to Stat 1510 Research Project
Style for Research Reports in Statistics
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.
The numbers in the picture follow the table below:
Yes No UndecidedOther
Republican
IndependentDemocrat
xSquared= 11.4411
P-value= .0756
df= 6Alpha= 0.05
CHI-Squared Test of Independence expected values: Violation if more that 20% are < 5.
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.
The numbers in the picture follow the table below:
Yes No Undecided
OtherRepublican
Independent
Democrat
xSquared= 4.8095
P-Value= .5684df= 6
CHI-Squared Test of Independence expected values: Violation if more that 20% are < 5.
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
The numbers in the picture follow the table below:
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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