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Owner: abarish274
Created: Dec 6, 2018
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PHASE THREE: Flagler College Fall 2018 Students and Tattoos
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On the first phase of this project, we began a study of a sample of 150 Flagler College students from the fall semester of 2018 about their opinions on tattoos, and whether or not they had them. In the second phase, the same sample was divided into two smaller samples. The two groups are the sample of Flagler College students who have tattoos and the sample of students who do not have tattoos. Of 150 students sample, 90 students did not have tattoos, while 60 students did. Out of 150 students, 60% do not have tattoos. A bar chart representing the two samples is presented below.







On this phase of the report, attention will be given to whether or not students have tattoos.

First, methods of statistical inference will be used to determine if the sample results indicate that the majority of the population of all Flagler College students do not have tattoos.  A hypothesis test will first be run to find statistical evidence of majority and then a confidence interval will be created to estimate the percentage of the population of Flagler College students who do not have tattoos.
Second, the sample results will also be used to determine if the parents of the population of all tatted students and the population of all untatted students at Flagler College have a statistically significant chance of having tattoos.  Again, a hypothesis test will be run to find statistical evidence of a difference and then a confidence interval will be created to estimate the difference in the percentage of the population of tatted and untatted students who have tatted parents.

Hypothesis Test #1 - A Claim of Majority



Of the 150 students sampled, 94 did not have tattoos, therefore the majority of students, 62%, had untatted parents. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted. The parents will be referred to as tatted or untatted parents. These sample results will be used to test the claim that the majority of the population of Flagler College students do not have tattoos at a significance level of .05. A pie chart of the data is given below.







Of the 150 students sampled, 90 did not have tattoos, therefore the majority of students, 60%, had no tattoos. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted.



Hypothesize

Null: fifty percent of all Flagler College students did not have tattoos.

Alternate: Less than 50% of all Flagler College students have tattoos.



Prepare

Random Sample- Not necessarily because the students that are in statistics class generally are younger students getting their general education classes out of the way. However, for the sake of this assignment, we will assume that it is.

Large Sample – Since np0 = (150) (0.50) = 75 > 10 and n(1-p0) = (150) (0.50) = 75 > 10 are both true statements, the sample is large.



Big Population- Since 10n= (10) (150)=1500 < 2500, the population is big. Flagler College has a population of approximated 2500 students



Independence within Sample- Yes, the responses were taken in ways that prove that they are independent of each other.



Compute








On the first phase of this project, we began a study of a sample of 150 Flagler College students from the fall semester of 2018 about their opinions on tattoos, and whether or not they had them. In the second phase, the same sample was divided into two smaller samples. The two groups are the sample of Flagler College students who have tattoos and the sample of students who do not have tattoos. Of 150 students sample, 90 students did not have tattoos, while 60 students did. Out of 150 students, 60% do not have tattoos. A bar chart representing the two samples is presented below.


 



On this phase of the report, attention will be given to whether or not students have tattoos.

First, methods of statistical inference will be used to determine if the sample results indicate that the majority of the population of all Flagler College students do not have tattoos.  A hypothesis test will first be run to find statistical evidence of majority and then a confidence interval will be created to estimate the percentage of the population of Flagler College students who do not have tattoos.
Second, the sample results will also be used to determine if the parents of the population of all tatted students and the population of all untatted students at Flagler College have a statistically significant chance of having tattoos.  Again, a hypothesis test will be run to find statistical evidence of a difference and then a confidence interval will be created to estimate the difference in the percentage of the population of tatted and untatted students who have tatted parents.

Hypothesis Test #1 - A Claim of Majority


Of the 150 students sampled, 94 did not have tattoos, therefore the majority of students, 62%, had untatted parents. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted. The parents will be referred to as tatted or untatted parents. These sample results will be used to test the claim that the majority of the population of Flagler College students do not have tattoos at a significance level of .05. A pie chart of the data is given below.


 


Result 2: Pie Chart with Data-




Of the 150 students sampled, 90 did not have tattoos, therefore the majority of students, 60%, had no tattoos. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted.


Hypothesize

Null: fifty percent of all Flagler College students did not have tattoos.

Alternate: Less than 50% of all Flagler College students have tattoos.


Prepare

  1. Random Sample- Not necessarily because the students that are in statistics class generally are younger students getting their general education classes out of the way. However, for the sake of this assignment, we will assume that it is.

  2. Large Sample – Since np0 = (150) (0.50) = 75 > 10 and n(1-p0) = (150) (0.50) = 75 > 10 are both true statements, the sample is large.


  1. Big Population- Since 10n= (10) (150)=1500 < 2500, the population is big. Flagler College has a population of approximated 2500 students


  1. Independence within Sample- Yes, the responses were taken in ways that prove that they are independent of each other.


Compute


 





p : Proportion of successes

H0 : p = 0.5

HA : p > 0.5


Interpret
Since the p-value (.9928) is greater than the level of significance of .05, there is not sufficient evidence to reject the null hypothesis.
Results 3: One sample proportion summary hypothesis test- Distraction


Confidence Interval #1 - Estimating the Population Proportion



Compute



 


Interpret


We are 90% confident that between 33.4% and 46.6% of all Flagler College students find that their parents do not have tattoos, that attend Flagler College.


Hypothesis Test #2- A Claim of the Difference between two Population Proportions


A contingency table was created to compare the differences between tatted and untatted students based on whether or not their parents were tatted.


 


A hypothesis test will be used to determine if this difference is statistically significant for the population of students at Flagler College. This test will run at a level of significance of 0.05.


Hypothesize


Null: There is no difference in the proportion of the population of students whose parents do not have tattoos and the proportion of the population of students whose parents do have tattoos.

Alternate: There is a difference in the proportion of the population of students whose parents do not have tattoos and the proportion of the population of students whose parents do have tattoos.


Based on the alternate hypothesis, this is a two tailed test.


 


 



 




Result 1: Result 1: Tattooed and Untattooed Students Sampled   [Info]
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Result 2: Result 2: Pie Chart With Data - Do Your Parents Have Tattoos?   [Info]
Right click to copy

Result 3: Result 3: One Sample Proportion Summary Hypothesis Test - Tattoos   [Info]

One sample proportion summary hypothesis test:


p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:
ProportionCountTotalSample Prop.Std. Err.Z-StatP-value
p601500.40.040824829-2.44948970.9928

Result 4: Result 4: One Sample Proportion Summary Confidence Interval - Tattoos   [Info]

One sample proportion summary confidence interval:


p : Proportion of successes
Method: Standard-Wald

90% confidence interval results:
ProportionCountTotalSample Prop.Std. Err.L. LimitU. Limit
p601500.40.040.334205850.46579415

Result 5: Result 5: Contingency Table (with data) - Tattoo vs. Parents with tattoos   [Info]

Contingency table results:


Rows: Tattoo
Columns: Parents with Tattoo
NoYesTotal
No662490
Yes283260
Total9456150

Chi-Square test:


StatisticDFValueP-value
Chi-square110.9422490.0009

Result 6: Result 6: Two Sample Proportion Summary Hypothesis Test - Tattoos vs. Parents with Tattoos   [Info]

Two sample proportion summary hypothesis test:


p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 ≠ 0

Hypothesis test results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.Z-StatP-value
p1 - p260150561500.0266666670.0562323220.474223110.6353

Result 7: Result 7: Two Sample Proportion Summary Confidence Interval - Tattoos vs. Parents with Tattoos   [Info]

Two sample proportion summary confidence interval:


p1 : proportion of successes for population 1
p2 : proportion of successes for population 2
p1 - p2 : Difference in proportions

95% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p260150561500.0266666670.056211242-0.0835053430.13683868

Data set 1. Flagler College Students and Tattoos - Ariel and S   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82822">PHASE THREE: Flagler College Fall 2018 Students and Tattoos</A>

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