Phase Three: Flagler College Diversity in 20182019
Introduction:
On the first phase of this project, the student body’s opinion on diversity at Flagler College was observed. Students from fall semester 2018 were surveyed. In the second phase, the same number of students was sampled, they were divided into two groups those who do not think the Flagler College student body is diverse and the sample of Flagler College students who do think the student body is diverse. There are 61 people who say that the student body is not diverse and 89 who say that the student body is diverse. A bar chart representing the two samples is presented below.
On this phase of the report, underlining the opinion of Flagler College students on diversity dependency on the number of countries visited by each student.
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 there is diversity in the student body depending on the number of countries visited. 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 opinion on diversity depending on the number of countries visited.
Second, the sample results will also be used to determine if the opinion of the population of Flagler College students is affected by the diversity of their hometown. 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 opinion of Flagler College students depending on the diversity of their hometown.
Hypothesis Test #1
In the sample of 150 students, 216 reported that the student body was not diverse depending on the number of countries they had visited. That is a minority, 42.94% of the students said that the student body was not diverse. 287 students said that the student body is diverse, with a 57.06%. These sample results will be used to test the claim that the majority of the student body believe that Flagler College is diverse at a level of significance of 0.05. A pie chart of the data is given below.
Hypothesize
Null:Fifty percent or of all Flagler College students believe that the student body is diverse.
Alternative: More than 50% of all Flagler College students believe that the student body at Flagler College is diverse.
Based on the alternate hypothesis, this is a rightsided test.
Prepare

Random Sample  The sample is random to a certain extent because it is selecting stats students

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

Big Population  Since 10n = (10)(150) = 1500 < 25000, the population is big. Flagler College population is approximately 25000 students.

Independence within the sample  Yes, the student responses were taken in such a way that their responses were independent of each other.
Compute
One sample proportion summary hypothesis test:p : Proportion of successes H_{0} : p = 0.5 H_{A} : p > 0.5 Hypothesis test results:

Interpret
Since the pvalue (0.5) is more than the level of significance of 0.05, the null hypothesis fails to reject. Therefore, in conclusion, there is insufficient evidence to support the claim that the majority of all Flagler College students surveyed believe that the student body is diverse.
Confidence Interval #1
The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that the student body is diverse. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that the student body is diverse. Since a onetailed test with a level of significance of 0.05 was run, a 90% confidence interval will be created.
Prepare

Random Sample with Independent Observation  The sample is random and independent to a certain extent because it is selecting stats students.

Large Sample  Since n*phat = (150) (0.57057) = 86> 10 and n* (1phat) = (150)(10.57057) = 64> 10, the sample is large enough.

Big Population  Since `0n = (10)(150) = 1500 < 25000, the population is big. Flagler College population is approximately 25000 students.
Compute
One sample proportion summary confidence interval:p : Proportion of successes Method: StandardWald 90% confidence interval results:

Interpret
We are 90% confident that between 43.3% and 56.7% of all Flagler College students find that the student body is diverse. This is not the majority of all Flagler College students because the lower limit of the confidence interval is below 50%. Also, zero is not in the confidence interval, 0.433 and 0.567 are both positive numbers and greater than zero. The population parameter is all Flagler College students.
Hypothesis Test #2 
A contingency table was created for the purpose of comparing the opinions of Flagler College students on the diversity of Flagler College’s student body, depending on the diversity of their hometown. The following contingency table compares the diversity of the student body and diversity of their hometown. Overall, 51 out of the 150 students surveyed believe there is no diversity in their hometown, while only 99 students believe the student body is diverse depending on their hometown. Thus, 66% (99/150) of all the students surveyed feel the student body is diverse. Therefore, the majority of the students surveyed feel that Flagler College has a diverse student body. Of the 61 students who believe the student body is diverse, 23 feel that the student body also lacks diversity and of the 89 students who believe the that their hometown is diverse, 28 feel that there is little diversity of the student body. That is, 37.7% (23/61) of the student who feel that the student body and their hometown is not diverse. While 31.5% (28/89) of the students who came from a diverse hometown believe the student body lacks diversity. Thus, approximately 6.2% more students feel their hometown and the student body are not diverse.
Contingency table results:Rows: Diverse Student Body Columns: Diverse Hometown
ChiSquare test:

A hypothesis test will be used to determine if the opinion of the student body is diverse depending on the student body hometown. 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 students who lived in a diverse hometown and who believed that the student body is diverse.
Alternative: There is a difference in the proportion of the population of students who believe they lived in a diverse hometown and that the student body is diverse.
Prepare

Large Samples  It is found that the sample proportion is phat = (x1+x2)/(n1n2) = (38+61) (61+89) = 99/150 = 0.66
Sample 1: Since n1*phat (61)(0.66) = 40.26 >10 and n1*(1  phat) = (61) (0.34) = 20.74> 10, sample one is large
Sample 2: Since n1*phat =(89)(0.66) = 58.74 > 10 and n1*(1  phat) = (89)(0.34) = 30.26 > 10, sample two is large

Random Samples  The sample is random and independent to a certain extent because it is selecting stats students.

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

Independence between samples  Yes, there is no relationship between the student's diversity and the diverse hometown.
Compute
Two sample proportion summary hypothesis test:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions H_{0} : p_{1}  p_{2} = 0 H_{A} : p_{1}  p_{2} ≠ 0 Hypothesis test results:

Interpret
Since the pvalue = 0.4278 it is more than the level of significance of 0.05, the null hypothesis fails to reject. Therefore, in conclusion, there is not sufficient evidence that there exists a difference in the proportion of the population of Flagler College students who believe the population of students at Flagler is diverse.
Confidence Interval #2
The hypothesis test gave us sufficient evidence that there is a significant difference in the opinion that the diversity of Flagler College depends on the diversity of their hometown. Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions cannot be equal. Since a twotailed test with a level of significance of 0.05 was run, a 90% confidence interval will be created.
Prepare

Random Samples with Independent Observations  Again, the sample is random to a certain extent because it is selecting stats students

Large Samples  Sample One: Since n1*phat1 = (61)(0.66) = 40.26 > 10 and n1*(1 
phat1) = (61)(1 – 0.66) = (61)(0.34) = 20.74 > 10, sample one is large.
Sample Two: Since n2*phat2 = (89)(0.377) = 33.5 > 10 and n2*(1  phat2) = (89)(10.377) = (89)(0.623) = 55.4 >10, sample two is large.

Big Populations  Recall, Flagler College has a population of appropriately 2500
students. Since we are unsure what overall percentage of the students are or are not affected socially by social media, we will assume 50% are and 50% are not. Hence, there are approximately (0.50)(2500) = 1250 students who are Social Students and (0.50)(2500) = 1250 students who are Unsocial Students in the population.
Population One: Since 10n1 = (10)(61) = 610 <1250 population one is big
Population two: Since 10n2 = (10)(89) = 890 < 1250 population two is big

Independent Samples Yes, the student's responses were taken in such a way that their responses were independent of each other.
Compute
Two sample proportion summary confidence interval:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions 90% confidence interval results:

Interpret
The confidence interval contains positive and negative values, (also contains 0); this indicates that the percentage of the population of Students who believe that the student body is diverse and came from a diverse hometown could be equal to each other. Thus, I am 90% confident that the percentage of all students who feel the student body is diverse is between 19.3% and 6.8%, meaning that there is no significant difference in the proportion of the population of students who lived in a diverse hometown and who believed that the student body is diverse. The population parameter is identified as all the Flagler College students.
Conclusion
In this report, the sample provided evidence that the number of students who think
Flagler College is diverse is between 43.3% and 56.7% out of all students who attend Flagler. In addition, the sample also provided evidence of students from diverse hometowns who do believe the student body is diverse. The estimation made within this sample came to a conclusion that 19.3% and 6.8% more of all Flagler College students that came from diverse hometowns believed the student body of Flagler is also diverse. The benefits of having a diverse student body of any college campus are to help with the sharing of cultures, points of views, and the simplicity of accepting people of different backgrounds. Hence, it is not surprising to see that the majority of students believe the student is diverse.
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