Introduction:
On the first phase of this project, flagler college students were sampled regarding Flagler College and diversity. The data was gathered in the fall 2017 and spring 2018 where about 150 students were surveyed. In the second phase, the same sample of 150 students was divided into two smaller samples which were female and male. There are 74 of the 101 females believe that the Flagler College campus activities are diverse and 39 of the 49 males do not believe that the Flagler College campus activities are diverse. The bar graph below shows that 67.3% of survey takers were female and 32.7% were male.
In this phase of the report, the opinion of the students regarding diversity in campus activities will be investigated. The first step will be hypothesis testing. A hypothesis test will be run to test that the majority of all Flagler College students believe that the Flagler College campus activities are diverse. Then a confidence interval will be created to estimate the proportion of all Flagler College students who believe that the Flagler College campus activities are diverse.
A second hypothesis test will be made to determine if there is a difference in the proportion of all females and proportions of all males at Flagler College who believe that the Flagler College campus activities are diverse. Then a confidence interval will be made to estimate the difference in the percentage.
Hypothesis Test #1 – A Claim of Majority
In the sample of 150 students, 113 out of the 150 (75.33%) students sampled believe that the Flagler College campus activities are diverse. That is, the majority, 73.33% of the students sampled expressed that they believe Flagler College campus activities are diverse. These results will be used to test the claim that the majority of the population of Flagler College students think that campus activities are diverse at a level of significance of 0.05. A bar chart of the data is shown below.
Hypothesize:
Null: Fifty percent of all Flagler College students believe that Campus Activities is diverse.
Alternate: More than 50% of all Flagler College students believe that Campus Activities 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 = (113) (0.50) = 56.5 > 10 and n(1p0) = (113) (0.50) = 56.5 > 10 are both true statements, the sample is large.
3. Big Population – Since 10n = (10)(113) = 1130 < 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.
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 (<0.0001) is less than the level of significance 0.05, the null hypothesis will be rejected. Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students feel that Flagler College campus activities is diverse.
Confidence Interval #1 – Estimating the Population Proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that Flagler College campus activities is diverse. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that Flagler College campus activities 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 = (113)(0.7533) = 85.1 > 10 and n*(1 – phat) = (113)(1 – 0.7533) = (113)(0.2467) = 27.9 > 10, the sample is large.
3. Big Population – Since 10n = (10)(113) = 1130 < 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:

Interpret
We are 90% confident that between 69.5% and 81,1% of all Flagler College students find that Flagler College campus activities is diverse. 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 female and male students regarding the Flagler College campus activities diversity. Of the 101 females, 74 believe that the Flagler College campus activities are diverse and of the 49 males 39 believe that the Flagler College campus activities are diverse. That is, 73.3% (74 female students out of 101) of the female students believed that Flagler College campus activities are diverse and 79.6% ( 39 male students out of 49) male students believed that Flagler College campus activities are diverse.
With an approximately 5% difference in these percentage, the sample gives some reason to believe that the population of Flagler College students as a whole believe that Flagler College campus activities is diverse.
Contingency table results:
Rows: Gender Columns: Campus Activity Diversity
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 female students at Flagler College and the proportion of the population of male Students at Flagler College who feel Flagler College campus activities are diverse.
Alternate: There is a difference in the proportion of the population of female students at Flagler College and the proportion of the population of male Students at Flagler College who feel Flagler College campus activities are diverse.
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) = (74 + 39)/(101 + 49) = 113/150 = 0.7533
Sample One (females): Since n1*phat = (101)(0.7533) = 76.1 > 10 and
n1*(1  phat) = (101)(1 – 0.7533) = (101)(0.2467) = 24.9 > 10, sample one is large.
Sample Two (males): Since n2*phat = (49)(0.7533) = 36.9 > 10 and
n2*(1  phat) = (49)(1 – 0.7533) = (49)(0.2467) = 12.1 > 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 female and the male Students.
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 = 0.3994 is more than the level of significance of 0.05, the null hypothesis will not be rejected. Therefore, there is sufficient evidence that there exists a no difference in the proportion of the population of female students at Flagler College and the proportion of the population of male students at Flagler College who feel Flagler College Activities are diverse.
Confidence Interval #2 –Estimate the Difference between two Population Proportions
The hypothesis test gave us sufficient evidence that there isn’t a significant difference in the opinion that Flagler College campus activities are diverse between the population of female students at Flagler College and the population of male 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 (females): Since n1*phat = (101)(0.7533) = 76.1 > 10 and
n1*(1  phat) = (101)(1 – 0.7533) = (101)(0.2467) = 24.9 > 10, sample one is large.
Sample Two (male): Since n2*phat = (49)(0.7533) = 36.9 > 10 and
n2*(1  phat) = (49)(1 – 0.7533) = (49)(0.2467) = 12.1 > 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 of opinion that Flagler College campus activities are or are not diverse, we will assume 50% are and 50% are not. Hence, there are approximately (0.50)(2500) = 1250 students who are female Students and (0.50)(2500) = 1250 students who are male Students in the population.
Population One (females): Since 10n1 = (10)(101) = 1010 < 1250, population one is big.
Population Two (male): Since 10n2 = (10)(49) = 490 < 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.
4. Independence between Samples – Yes, there is no relationship between the female and the male Students.
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 not completely negative; this indicates that the percentage of the population of all Female Students believe Flagler College campus activities are diverse is greater than the percentage of the population of all Male Students who believe Flagler College campus activities are diverse. Thus, I am 95% confident that the percentage of all Female Students who believe Flagler College Campus activities are diverse is between 20.5% and 7.9% greater than the percentage of all male students who believe Flagler College campus activities are diverse.
Conclusion
Diversity has become an important topic over the years. Furthermore, Flagler College makes it a point to have a very diverse campus and it is noticeable in the percentage of international students as well as staff on campus. To make diversity a normal thing on campus, activities are held. In this report the sample proved that the majority of both gender believe campus activities are diverse on Flagler College campus. It was estimated that between 69.5% and 81.1% of all Flagler College students find that Flagler College campus activities is diverse. Campus diversity topic is interesting to me being that I am international myself and enjoy meeting people from all different places as well as learning more about cultures and languages.
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