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PHASE THREE: College Education and Clubs at Flagler College
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 PHASE THREE: College Education and Clubs at Flagler College
 
Introduction:
 
On the first phase of this project, the importance of a college education of a sample of 150 Flagler College students from fall semester 2018 was explored.  In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as “GPA centered” and “GPA indifferent” students.  The term “GPA centered” defined the sample of those Flagler College students whom do not believe their college GPA will have an impact on future job prospects, and the term “GPA centered” defined the sample of those Flagler College students who do think GPA will affect future job prospects.  There are 89 GPA centered and 61 GPA indifferent l Students sampled.  A bar graph representing the two samples is presented below.
 

Result 1: Bar Plot With Data GPA and future job employment   [Info]
Right click to copy

 
On this phase of the report, attention will be given to students’ opinions about whether joining a college club is important to their college education. 
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 Joining a college club is important to their college education.  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 college clubs have importance.
Second, the sample results will also be used to determine if the opinion of the population of all GPA centered and the population of all GPA indifferent Students at Flagler College have a statistically significant difference of opinion regarding the importance of college clubs to their collegiate experience.  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 GPA centered and GPA indifferent students who findcollege clubs to be significant to their college experience.
 
Hypothesis Test #1 – A Claim of Majority
In the sample of 150 students, 89 reported that GPA does infact affect their future job prospects.  That is, the majority, 59.33%, of the students sampled expressed that GPA matters.  These sample results will be used to test the claim that the majority of the population of Flagler College students view college clubs as important at a level of significance of 0.05  A pie chart of the data is given below.
 

Result 2: Pie Chart With Data college club   [Info]
Right click to copy

 
Hypothesize
              Null: Fifty percent of all Flagler College students believe that college clubs are important to their college education.
              Alternate: More than 50% of all Flagler College students believe that college clubs are important to their college experience
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- gpa importance in job acquisition phase 3   [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
p891500.593333330.0408248292.28619040.0111

 
Interpret
Since the p-value (<0.0111) 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 college clubs are important to their education.
 
Confidence Interval #1 – Estimating the Population Proportion
 
              The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that college clubs are important.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that college clubs are important.  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)(0.59333333) = 88.99 > 10 and n*(1 – phat) = (150)(1 –0.59333333) = (150)(0.4066) = 61 > 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
 

Result 4: One sample proportion summary confidence interval-gpa impoertance in job acquisition phase 3   [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
p891500.593333330.0401072640.527362760.65930391

 
Interpret
 
We are 90% confident that between 52.73% and 65.93% of all Flagler College students find that college clubs are important.  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 GPA centered and the GPA indifferent Students regarding the importance of college clubs.  Of the 89 GPA centered, 68 felt that college clubs were important-and of the 61 GPA indifferent Students, 43 felt college clubs were important.  That is, 76.40% (68 students out of 89) of the GPA centered students felt college clubs were important and 70.49% (43 students out of the 61 students) of the GPA indifferent Students felt college clubs were important.  With an approximately 6% difference in these percentages, the sample gives some reason to believe that the population of GPA centered students at Flagler College and the population of GPA indifferent Students at Flagler College differ in their opinion that college clubs have value.
 

Result 5: Contingency table of students attending a college club and those who believe gpa is significant in g   [Info]

Contingency table results:


Rows: College GPA importance in job acquisition
Columns: College Club
NoYesTotal
No184361
Yes216889
Total39111150

Chi-Square test:


StatisticDFValueP-value
Chi-square10.657648590.4174

 
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 GPA centered Students at Flagler College and the proportion of the population of GPA indifferent Students at Flagler College who feel college clubs are important to their college education.
 
Alternate: There is a difference in the proportion of the population of GPA centered Students at Flagler College and the proportion of the population of GPA indifferent Students at Flagler College who feel college clubs are and important part of the college experience.
 
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) = (68 + 43)/(89 + 61) = 111/150 = 0.74
Sample One (GPA centered): Since n1*p-hat = (89)(0.74) = 65.86 > 10 and
n1*(1 - p-hat) = (89)(1 – 0.74) = (89)(0.26) = 23.14 > 10, sample one is large.
Sample Two (GPA indifferent): Since n2*p-hat = (61)(0.74) = 45.14 > 10 and
n2*(1 - p-hat) = (61)(1 – 0.74) = (61)(0.26) = 15.86 > 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 GPA centered Students and the GPA indifferent Students.
 
Compute
 

Result 6: Two sample proportion summary hypothesis test-importance of gpa in job acquisition and college club   [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 - p243616889-0.0591269110.072910192-0.810955360.4174

 
Interpret
Since the p – value = 0.4174 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 GPA centered students at Flagler College and the proportion of the population of GPA indifferent Students at Flagler College who feel College clubs are important.
 
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 college clubs are important  between the population of GPA centered students at Flagler College and the population of GPA indifferent 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 (GPA centered): Since n1*p-hat1 = (89)(0.593) = 48 > 10 and
n1*(1 - p-hat1) = (89)(1 – 0.76) = (89)(0.24) = 21.36 > 10, sample one is large.
Sample Two (GPA indifferent): Since n2*p-hat2 = (69)(0.855) = 59 > 10 and
n2*(1 - p-hat2) = (61)(1 – 0.70) = (61)(0.3) = 18.3 > 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 by college clubs, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are GPA centered and (0.50)(2500) = 1250 students who are GPA indifferent Students in the population.
Population One (GPA centered): Since 10n1 = (10)(89) = 890 < 1250, population one is big. 
Population Two (GPA indifferent): Since 10n2 = (10)(61) = 610 < 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-gpa importance in job acquisition and college club   [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 - p243616889-0.0591269110.073726508-0.203628210.08537439

 
Interpret
 
This confidence interval is completely positive; this indicates that the percentage of the population of all GPA centered students who feel college clubs are important is more than of the population of all GPA indifferent students who feel college clubs are important that the percentage of all GPA indifferent students who feel college clubs are important is between 8.53% and 20.36% lesser than the percentage of all GPA centered students who feel college clubs are important.
 
Conclusion
 
The school systems set in place within the United States all push their students to reach a certain standard, often times that standard is measured through their GPA. Many students define themselves based off of that number. However, some choose to not let that be the thing that labels them, and reject some of the validity within a GPA based system. Many also find that College Clubs form a vital part of their college experience-a place for them to make friends and find a community.  In this report, the sample provided evidence that the majority of all Flagler College students find that there is importance in attending a college club; that it adds to the experience of being at Flagler College.  In fact, it was estimated that between  52.73% and 65.93% of all Flagler College students find that college clubs are important.  Furthermore, it was found that there is statistical evidence that those students who feel GPA centered are more likely to say college clubs are important
 
  It was estimated that between 8.53% and 20.36% more of all Flagler College students with feelings of being GPA indifferent were not in favor of college clubs than all other Flagler College students.  This is natural association to me.  I feel that if someone were to not really take their GPA into consideration, then they could potentially not really have much interest in school extracurriculars, or anything extra they could probably add to their resume.
Typically college clubs are a way in which college students can find others that share the same interests, values, and cultures. They are a way to create a community for oneself. It does not surprize me that the majority find that college clubs are an important aspect of the college experience, I know for me personally club UNITY has been a really positive provider of friends and colleagues. Perhaps making some of the club meetings at flagler college count for co-curriculars will heighten the amount of attendance and will further create connections within the student population.
 
 

Data set 1. Garcia-Ashe-Latorre-Sampled from Flagler College S   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=87124">PHASE THREE: College Education and Clubs at Flagler College</A>

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