PHASE THREE: Flagler College Students and Diversity
Introduction:
On the first phase of this project, a sample of 150 on the diversity of flagler college students from fall semester 2018 was explored. In phase two of the report, this same sample of 150 students will be divided into two smaller samples. The two samples are the sample of Flagler College students who do not believe the student body to be diverse and the sample of flagler students who do believe the student body is diverse. There are 63 students who believe the student body to not be diverse and there are 87 who believe that the student body is diverse. A bar chart representing these two samples is presented below.
On this phase of the report, attention will be given to students’ opinions about if they believe the campus to be diverse.
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 the campus is diverse. 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 that the campus is diverse.
Second, the sample results will also be used to determine if the opinion of the population of all Students at Flagler College who believe the campus to be diverse and the population of all Students at Flagler College who believe that the campus is not diverse have a statistically significant difference of opinion regarding the belief of diversity. 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 students who believe the campus to be diverse vs. the students who do not believe the campus to be diverse.
Hypothesis Test #1  A claim of Majority
In the sample of 150 students, 87 reported that they believed that the student body to be diverse. That is, the majority, 58%, of the students sampled expressed that they believed the student body to be diverse. These sample results will be used to test the claim that the majority of the population of Flagler College students believe that the student body is diverse at a level of significance of 0.05 A pie chart of the data is given below.
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Hypothesize
Null: Fifty percent of all Flagler College students believe that the student body is diverse.
Alternate: More than 50% of all Flagler College students believe that the student body is diverse.
Based on the alternate hypothesis, this is a rightsided 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(1p0) = (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
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 (0.025) 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 the student body at Flagler College is diverse.
Confidence Interval #1 – Estimating the Population Proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College students who believe the student body to be 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 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)(0.58) = 87 > 10 and n*(1 – phat) = (150)(1 – 0.58) = (150)(0.42) = 63 > 10, 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.
Compute
One sample proportion summary confidence interval:
p : Proportion of successes Method: StandardWald 90% confidence interval results:

We are 90% confident that between 40.3% and 51.4% of all Flagler College students believe that the student body is diverse. This is not the majority of all Flagler Students.
Hypothesis Test #2 – A Claim of the Difference between two Population Proportions
A contingency table was created to compare the opinions of students who believe the student body to be diverse or not regarding the students who believe that Flagler offers diverse campus activities. Of the 87 students who believe that the student body is diverse, 81 felt that the campus activities were also diverse and of the 63 student who believed the student body to not be diverse , 42 felt that the campus activities are diverse That is, 93.1% (81 students out of 87 students) of the students who believe the student body to be diverse also believe that the campus activities are also diverse and 66.7% (42 students out of the 66 students) of the students who did not believe that the student body was diverse, believed that the campus activities at Flagler College are diverse. With an approximately 25% difference in these percentage, the sample gives some reason to believe that the population of Students who believe the student body is diverse at Flagler College and the population of Students who believe that the student body is not diverse at Flagler College differ in their opinion that the campus activities at flagler are diverse.
Contingency table results:
Rows: Diverse Student Body Columns: Diverse Campus Activities
ChiSquare test:

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 Students who believe the student body to be diverse at Flagler College and the proportion of the population of Students who believe the student body to not be diverse at Flagler College who feel that the campus activities at flagler college to be diverse.
Alternate: There is a difference in the proportion of the population of diverse students at Flagler College and the proportion of the population of non diverse students at Flagler College who feel Flagler College offers diverse campus activities.
Based on the alternate hypothesis, this is a two tailed test.
Prepare:
1. Large Samples – It is found that the pooled sample proportion is
phat = (x1 + x2)/(n1 + n2) = (42 + 81)/(63 + 87) = 87/150 = 0.58
Sample One (Social Students): Since n1*phat = (63)(0.58) = 36.54 > 10 and
n1*(1  phat) = (81)(1 – 0.7133) = (63)(0.42) = 26.46 > 10, sample one is large.
Sample Two (Unsocial Students): Since n2*phat = (87)(0.58) = 50.46 > 10 and
n2*(1  phat) = (69)(1 – 0.7133) = (87)(0.42) = 36.54> 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 Social Students and the Unsocial Students.
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 p – value = 0.0001 is less than the level of significance of 0.05, the null hypothesis will be rejected. Therefore, there is sufficient evidence that there exists a difference in the proportion of the population of Students who believe the student body to be diverse at Flagler College and the proportion of the population of Students who don't not believe the student body to be diverse at Flagler College who feel that the campus activities at Flagler College are diverse.
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 the campus activities at flagler are diverse between the population of Students who beleive the student body to be diverse at Flagler College and the population of Students who do not beleive the student body to be diverse 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 (Social Students): Since n1*phat1 = (87)(0.93) = 81> 10 and
n1*(1  phat1) = (87)(1 – 0.93) = (87)(0.07) = 6.09 > 10, sample one is large.
Sample Two (Unsocial Students): Since n2*phat2 = (63)(0.666) = 42> 10 and
n2*(1  phat2) = (63)(1 – .666) = (63)(0.145) = 21.04> 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 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 Students who believe the student body to be diverse and (0.50)(2500) = 1250 students who are Students who do not believe the student body to be diverse in the population.
Population One (students who believe the student body to be diverse ): Since 10n1 = (10)(87) = 870 < 1250, population one is big.
Population Two (students who do not believe the student body to be diverse): Since 10n2 = (10)(63) = 630 < 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  Students who believe the student body to be diverse or not diverse vs the students who believe the campus activities to be diverse or not diverse
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 95% confidence interval results:

Interpret
This confidence interval is positive; this indicates that the percentage of the population of all Students who believe the student body to be diverse who feel that the campus activities are also diverse could be equal to the percentage of the population of all Students who believe the student body to not be diverse who feel that the campus activities at flagler are diverse. Thus, I am 95% confident that the percentage of all Students who believe that the student body is not diverse who feel that the campus activities are diverse is between 13.6% and 39.2% greater than the percentage of all Students who believe the student body is diverse and also believe that the campus activities are diverse.
Conclusion
Society has always valued the importance of having diversity around the world and on college campuses. In this report, the sample provided evidence that there was not a majority of all Flagler College students believe that the campus activities at flagler college to be diverse. In fact, it was estimated that between 40.3 % and 51. 4% of all Flagler College students believe that the campus activities are diverse. Furthermore, it was found that there is statistical evidence that those students who believed that the student body was not diverse also believed that the campus activities were diverse.. It was estimated that between 13.6% and 39.2% more of all Flagler College students with feelings that the student body is not diverse also believed that the campus activities are diverse more than all other Flagler College students.Having a diverse student body and campus activities helps form a whole community so that everyone feels like they are apart of it.
The underlying purpose of having diversity in a campus is to help with socialization and connecting people. It is interesting however, that those who did not believe the student body to be diverse also believe that the campus activities are diverse. Maybe a policy of that is put in forth to divide the diversity of students in classrooms should be made so that all students feel that the student body is diverse. It may help students feel more comfortable in their surroundings if they see people of the same ethnicity as them. Although enforcing such a policy that would be difficult, it is something to consider. On the other hand, dividing students into groups randomly each day and having them greet each other is a policy that I will continue to implement to possibly encourage student interaction and diversity. Times are always changing, but humans are social animals so hopefully having a more diverse campus will help people feel more welcomed and easier for them to fit in.
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