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Phase Three
Generated Apr 24, 2019 by ogarvey697

PHASE THREE: Flagler College Students and Tattoos in Spring 2019

PHASE THREE: Tattoos of Flagler College Students in Spring 2019

Introduction:

On the first phase of this project, a sample of 150 Flagler College students and their tattoos were explored in the spring semester of 2019. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as the “Male Students” and “Female Students.”  There are 26 Males and 74 Females sampled. A bar chart representing the two samples is presented below.

Result 1: Males and Females Sampled

On this phase of the report, attention will be given to students’ opinions about tattoos being socially accepted or not.

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 feel that tattoos are socially accepted.  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 feel tattoos are socially accepted.

Second, the sample results will also be used to determine if the opinion of the population of all Male Students and the population of all Female Students at Flagler College have a statistically significant difference of opinion regarding if tattoos are socially accepted or not. 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 Male Students and Female Students who find tattoos to be socially acceptable or not.

Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 96% reported that tattoos are socially accepted.  That is, the majority, 64%, of the students sampled expressed that tattoos are socially accepted.  These sample results will be used to test the claim that the majority of the population of Flagler College students view tattoos as socially acceptable at a level of significance of 0.05  A pie chart of the data is given below.

Result 2: Pie Chart With Data - Tattoos - Are they socially acceptable?

Hypothesize

Null: Fifty percent of all Flagler College students believe that tattoos are socially acceptable.

Alternate: More than 50% of all Flagler College students believe that tattoos are socially acceptable.

Based on the alternate hypothesis, this is a right-sided test.

Prepare

1. Random Sample – Frankly, probably not (but we hope it is representative).  However, to proceed, we will assume 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.

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

4. Independence within Sample – Yes, the student responses were taken in such a way that their responses were independent of each other.

Compute

Result 3: One sample proportion summary hypothesis test - Socially Acceptable

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Interpret

Since the p-value (<0.0003)is less than the level of significance of 0.05, the null hypothesis must be rejected.  Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students feel that tattoos are socially acceptable.

Confidence Interval #1 – Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that tattoos are socially acceptable.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe tattoos are socially acceptable.  Since a one tailed test with a level of significance of 0.05 was run, a 90% confidence interval will be created.

Prepare

1. Random Sample with Independent Observations – Again, probably not (but we hope it is representative).  However, to proceed, we will assume it is. Furthermore, yes, the student responses were taken in such a way that their responses were independent of each other.

2. Large Sample – Since n*phat = (150)(0.64) = 96 > 10 and n*(1 – phat) = (150)(1 – 0.64) = (150)(0.36) = 54 > 10, the sample is large.

3. Big PopulationSince 10n = (10)(150) = 1500 < 2500, the population is big.  Recall, Flagler College has a population of appropriately 2500 students.

Compute

Result 4: One sample proportion summary confidence interval - Socially Acceptable

Interpret

We are 95% confident that between 57.55%and 70.45% of all Flagler College students find that tattoos are socially acceptable.  This is certainly the majority of all Flagler College students.

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

A contingency table was created to compare the opinions of the Male Students and the Female Students regarding if tattoos are socially accepted or not.  Of the 39 Male Students, 37 felt tattoos were socially acceptable and of the 111 Female Students, 99 felt tattoos are socially acceptable. That is, 94.9% (37 students out of 39) of the Male Students felt social media was a distraction and 89.2% (99 students out of the 111 students) of the Female Students felt tattoos were socially acceptable.  With an approximately 5.7% difference in these percentage, the sample gives some reason to believe that the population of Male Students at Flagler College and the population of Female Students at Flagler College differ in their opinion that tattoos are socially acceptable.

Result 5: Contingency table (with data) - Male Vs. Socially acceptable

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 be run at a level of significance of 0.05.

Hypothesize

Null: There is no difference in the proportion of the population of Male Students at Flagler College and the proportion of the population of Female Students at Flagler College who feel tattoos are socially acceptable.

Alternate: There is a difference in the proportion of the population of Male Students at Flagler College and the proportion of the population of Female Students at Flagler College who feel tattoos are socially acceptable.

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

Prepare:

1.       Large Samples – It is found that the pooled sample proportion is

p-hat = (x1 + x2)/(n1 + n2) = (99 + 37)/(75 + 75) = 136/150 = 0.9066

Sample One (Male Students): Since n1*p-hat = (69)(0.7133) = 49.2 > 10 and

n1*(1 - p-hat) = (39)(1 – 0.7133) = (39)(0.2867) = 11.1813 > 10, sample one is large.

Sample Two (Female  Students): Since n2*p-hat = (111)(0.64) = 71.04 > 10 and

n2*(1 - p-hat) = (111)(1 – 0.64) = (111)(0.36) = 39.96> 10, sample two is large.

2. Random Samples – Again, probably not (but we hope they are representative).  However, to proceed, we will assume they are.

3. Independent Samples – Yes, the student responses were taken in such a way that their responses were independent of each other.

4. Independence between Samples – Yes, there is no relationship between the Male Students and the Female Students.

Compute

Result 6: Two sample proportion summary hypothesis test - Female Vs. Socially Acceptable

Interpret

Since the p – value = 1 is less than the level of significance of 0.05, the null hypothesis will fail to be rejected.  Therefore, there is not sufficient evidence that there exists a difference in the proportion of the population of Male Students at Flagler College and the proportion of the population of Female Students at Flagler College who tattoos are socially acceptable.

Confidence Interval #2 –Estimate the Difference between two Population Proportions

The hypothesis test gave us sufficient evidence that there is a significant difference in the opinion that tattoos are socially acceptable between the population of Male Students at Flagler College and the population of Female Students at Flagler College. Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions cannot be equal.  Since a two tailed test with a level of significance of 0.05 was run, a 95% confidence interval will be created.

Prepare

1. Random Samples with Independent Observations – Again, probably not (but we hope it is representative).  However, to proceed, we will assume it is. Furthermore, yes, the student responses were taken in such a way that their responses were independent of each other.

2. Large Samples

Sample One (Male Students): Since n1*p-hat1 = (111)(0.43) = 48 > 10 and

n1*(1 - p-hat1) = (111)(1 – 0.593) = (111)(0.407) = 45> 10, sample one is large.

Sample Two (Female Students): Since n2*p-hat2 = (69)(0.855) = 59 > 10 and

n2*(1 - p-hat2) = (39)(1 – 0.855) = (111)(0.145) = 16 > 10, sample two is large.

3. Big Populations – Recall, Flagler College has a population of appropriately 2500 students.  Since we are unsure what overall percentage of the students find tattoos socially acceptable or not, we will assume 50% find them socially acceptable and 50% do not find them socially acceptable.  Hence, there are approximately (0.50)(2500) = 1250 students who are Male Students and (0.50)(2500) = 1250 students who are Female Students in the population.

Population One (Male Students): Since 10n1 = (10)(39) = 810 < 1250, population one is big.

Population Two (Female Students): Since 10n2 = (10)(111) = 690 < 1250, population two is big.

4. Independent Samples – Yes, the student responses were taken in such a way that their responses were independent of each other.

Compute

Result 7: Two sample proportion summary confidence interval - Female Vs. Socially Acceptable

Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all Male Students who feel tattoos are socially acceptable is lessthan the percentage of the population of all Female Students who feel tattoos are socially acceptable.  Thus, I am 95% confident that the percentage of all Female Students who feel tattoos are socially acceptable is between 14.7% and 3.3% greater than the percentage of all Male Students who feel tattoos are socially acceptable.

Conclusion

Society has embraced tattoos and the fact that they might not be totally socially acceptable yet.  However, this is changing. In this report, the sample provided evidence that the majority of all Flagler College students find tattoos to be socially acceptable.  In fact, it was estimated that between 57.55%and 70.45% of all Flagler College students find that tattoos are socially acceptable.  Furthermore, it was found that there is statistical evidence that students specificallymale believe it is more socially acceptable to have tattoos thanfemalestudents.  It was estimated that between 14.7% and 3.3% more of all Flagler College students who thought tattoos were not socially acceptable were females than all other Flagler College students being male.  This is natural association to me. I feel tattoos are becoming more socially acceptable and that I am not alone in believing this (at least at Flagler).

The underlying purpose of tattoos are to help people express themselves creatively and enhance their natural beauty.  Flagler seems to be a creative school which has many expressive students. Hence, it is no surprise that Flagler students believe they are socially acceptable. Maybe hiring teachers with more tattoos would make tattoos seem even more socially acceptable, and may help students with tattoos feel more accepted.  Although hiring teachers with tattoos may cause controversy, it is something to consider because we would be adding creative diversity to Flagler. Times are always changing, but humans are creative animals so hopefully a balance between accepting tattoos and not accepting tattoos will be met with the next generations.

Data set 1. Responses to Tattoos - Spring 2019

Result 1: Bar Plot With Data\$\$\$\$   [Info]

Result 2: One sample proportion summary hypothesis test!!!!   [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
p961500.640.0408248293.42928560.0003

Result 3: One sample proportion summary confidence interval***   [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
p961500.640.0391918360.575535170.70446483

Result 4: Contingency table (with data)   [Info]

### Contingency table results:

Rows: Sample(Gender)
Columns: Sample(Tattoo Socially Accepted)
NoYesTotal
Female1299111
Male23739
Total14136150

### Chi-Square test:

StatisticDFValueP-value
Chi-square11.10130330.294
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Result 5: Two sample proportion summary hypothesis test   [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 = 0.5
HA : p1 - p2 > 0.5

Hypothesis test results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.Z-StatP-value
p1 - p2991113739-0.0568260570.05414945-10.2831341

Result 6: Two sample proportion summary confidence interval   [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 - p2991113739-0.0568260570.046001606-0.146987550.033335434