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PHASE THREE: Flagler College Student and Diversity in 2018-2019
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Phase Three: Flagler College Diversity in 2018-2019


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.

Result 1: Diverse Student Body   [Info]
Right click to copy


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.


Result 2: Diverse Student Body vs. Number of Countries Visited   [Info]
Right click to copy

 

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 right-sided test.


Prepare

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

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

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

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

 

Compute

Result 3: One Sample Hypothesis Test of Students Who Believe Student Body is Diverse   [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
p751500.50.04082482900.5


Interpret

Since the p-value (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 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 Observation -  The sample is random and independent to a certain extent because it is selecting stats students.

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

  3. Big Population - Since `0n = (10)(150) = 1500 < 25000, the population is big. Flagler College population is approximately 25000 students.


Compute

Result 4: One Sample Confidence Interval of Students Who Believe Student Body is Diverse   [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
p751500.50.0408248290.432849130.56715087


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.


Result 5: Contingency table of Diverse Student Body and Diverse Hometown   [Info]

Contingency table results:


Rows: Diverse Student Body
Columns: Diverse Hometown
NoYesTotal
No233861
Yes286189
Total5199150

Chi-Square test:


StatisticDFValueP-value
Chi-square10.628876610.4278



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

  1. Large Samples - It is found that the sample proportion is p-hat = (x1+x2)/(n1-n2) = (38+61) (61+89) = 99/150 = 0.66


Sample 1: Since n1*p-hat (61)(0.66) = 40.26 >10 and n1*(1 - p-hat) = (61) (0.34) = 20.74> 10, sample one is large


Sample 2: Since n1*p-hat =(89)(0.66) = 58.74 > 10 and n1*(1 - p-hat) = (89)(0.34) = 30.26 > 10, sample two is large


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

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

  3. Independence between samples - Yes, there is no relationship between the student's diversity and the diverse hometown.



Compute

Result 6: Two Sample Hypothesis test of Students From Diverse Hometowns Who Believe the Student Body is Divers   [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 - p238616189-0.0624424390.078740313-0.793017410.4278


Interpret

Since the p-value = 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 two-tailed test with a level of significance of 0.05 was run, a 90% confidence interval will be created.


Prepare

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


  1. Large Samples -  Sample One: Since n1*p-hat1 = (61)(0.66) = 40.26 > 10 and n1*(1 -

p-hat1) = (61)(1 – 0.66) = (61)(0.34) = 20.74 > 10, sample one is large.


Sample Two: Since n2*p-hat2  = (89)(0.377) = 33.5 > 10 and n2*(1 - p-hat2) = (89)(1-0.377) = (89)(0.623) = 55.4 >10, sample two is large.


  1. 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

  1. Independent Samples- Yes, the student's responses were taken in such a way that their responses were independent of each other.


Compute

Result 7: Two sample Confidence Interval of Students From Diverse Hometowns Who Believe Student body is Divers   [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

90% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p238616189-0.0624424390.079204445-0.192722160.06783728

 

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.


Data set 1. Balzell, Bascope, Camacho   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82751">PHASE THREE: Flagler College Student and Diversity in 2018-2019</A>

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