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Created: Dec 6, 2018
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Phase Three: Flagler College Students and Work Fall 2018
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PHASE THREE: Students and Work at Flagler College Fall 2018 

Introduction:
On the first phase of this project, the opinions of students and work was taken from a sample of 150 Flagler College students in the 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 the students who believed their school performance was “Compromised by Work” and the students who believe their school performance was “Uncompromised by Work”. The term “Compromised by Work” defines the students in the sample who believe that their school performance will be compromised with work. The term “Uncompromised by Work” defines the students in the sample who believe that work will not compromise their school performance. There are 54 “Compromised by Work” students, and 96 “Uncompromised by Work” students. A bar chart representing the two samples is given below.

Result 1: School Performance Compromised by Work   [Info]
Right click to copy

On this phase of the report, attention will be given to students’ opinions about them treating academics like a job.

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 treat academics like a job.  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 treat academics like a job.

Second, the sample results will also be used to determine if the opinion of the population of Compromised by work students and Uncompromised by work students at Flagler have a statistically significant difference of opinion of whether they treat academics like a job or not.  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 treat academics like a job.

Hypothesis Test #1 – A Claim of Majority

In sample 1 of 150 students, 115 reported that they treat academics like a job. That is the majority, 76.67% of the students expressed that they treat academics like a job. These sample results will be used to test the claim that the majority of the population of Flagler College students treat academics like a job at a level of significance of 0.05 A pie chart of the data is given below.

Result 2: Treat Academics like a job   [Info]
Right click to copy

Hypothesize

 Null: Fifty percent of all Flagler College students treat academics like a job.

Alternate: More than 50% of all Flagler College students treat academics like a job.

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: result 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
p1151500.766666670.0408248296.5319726<0.0001

Interpret

Since the p-value (<0.0001) 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 treat academics like a job.

Confidence Interval #1 – Estimating the Population Proportion

  The hypothesis test gives sufficient evidence that the majority of all Flagler College students treat academics like a job. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students that treat academics like a job. 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)(0.7667) = 115 > 10 and n*(1 – phat) = (150)(1 – 0.7667) = (150)(0.2333) = 35 > 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: result 4   [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
p1151500.766666670.0345339340.70986340.82346993

Interpret

We are 90% confident that between 71% and 82.3% of all Flagler College students treat academics like a job. 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 Compromised by Work students and the Uncompromised by Work students regarding whether the students treat academics like a job. Of the 96 Uncompromised by Work students, 70 teated academics like a job. Of the 54 Compromised by Work Students, 45 treated academics like a job. That is, 72.92% (70 students out of 96) of the Uncompromised by work students treated academics like a job, and 83.33% (45 students of out 54) of the Compromised by Work students treated academics like a job. With an approximately 10% difference in these percentages, the sample gives some reason the believe that the population of Uncompromised by Work students at Flagler College and the population of Compromised by Work students at Flagler College slightly differ in their opinion of whether they treat academics like a job.

 

Result 5: Contingency table (with data)   [Info]
Contingency table results:
Rows: School Performance Compromised by Work
Columns: Treat Academics like a Job
NoYesTotal
No267096
Yes94554
Total35115150

Chi-Square test:
StatisticDFValueP-value
Chi-square12.09627330.1477

 

A hypothesis test will be used to determine if the difference is statistically significant for the population of students at Flagler College who treat academics like a job. 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 Uncompromised by Work students at Flagler College and the proportion of the population of Compromised by Work students at Flagler College who treat their academics like a job.

Alternate: There is a difference in the proportion of the population of Uncompromised by Work students at Flagler College and the proportion of the population of Compromised by Work students at Flagler College who treat their academics like a job.

Based on the alternate hypothesis, this is a two tailed test.

Prepare:

 

 1.) Large Samples-

p-hat = (x1 + x2)/(n1 + n2) = ( 70 + 45 )/( 96 + 54 )= 115/150=  .7667

Sample One (Uncompromised by Work Students): Since n1*p-hat = (96)(.7667)= 73.60 > 10 and, 

n1*(1 - p-hat) =(96)(1 — .7667)= (96)(.2333) = 22.40 > 10, sample one is large.

Sample Two (Compromised by Work Students): Since n2*p-hat = (54)(.7667)= 41.40 > 10 and,

n2*(1 - p-hat) = (54)(1 —.7667) = (54)(.2333)= 12.60 > 10, sample two is large.

 

2.) Random Samples — We proceed to assume that the sample are random 

3.) Independent Samples — Yes, the students response taken in a way in which one student’s response is independent to another student’s response. 

4.) Independence between Samples — Yes, there is no relationship between the Compromised by Work students and Uncompromised by Work students.

Compute 

Result 6: result 6   [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 - p270964554-0.104166670.071945696-1.44785130.1477

 

Interpret: Since the p – value = 0.1477 is more than the level of significance of 0.05, the null hypothesis will not be rejected.  Therefore, there is not enough sufficient evidence that there exists a difference in the proportion of the population of students who Treat School Performance Compromised by Work at Flagler College and the proportion of the population of students who Treat Academics like a Job at Flagler College. 

 

 

 

Confidence Interval #2 –Estimate the Difference between two Population Proportions

The hypothesis test did not us enough suffiedeivnt evidence  that there exists a difference between the population of Uncompromised by Work students at Flagler College and the population of the Compromised by Work students at Flagler College. Therefore, a confidence interval will be created to estimate that there is not a difference and confirm that the two populations proportion could 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 (Uncompromised by Work students ): Since n1*p-hat1 = (96)(0.7292) = 70 > 10 and

n1*(1 - p-hat1) = (96)(1 – 0.7292) = (81)(0.2708) = 26 > 10, sample one is large.

Sample Two (Compromised by Work students): Since n2*p-hat2 = (54)(0.8333) = 45 > 10 and

n2*(1 - p-hat2) = (54)(1 – 0.8333) = (81)(0.1667) = 9 < 10, sample two is not large.

3. Big Populations – Recall, Flagler College has a population of appropriately 2500 students.  Since we are unsure what overall percentage of the students do or do not treat academics like a job, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Uncompormised by Work students and (0.50)(2500) = 1250 students who are Compromised by Work students in the population.

Population One (Uncompormised by Work students): Since 10n1 = (10)(96) = 960 < 1250, population one is big. 

Population Two (Compromised by Work students): Since 10n2 = (10)(54) = 540 < 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. 

Result 7: result 7   [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 - p270964554-0.104166670.06803769-0.237518090.029184755

 

Interpret: This confidence interval is both positive and negative; this indicates that the percentage of the population of all Students who believe School Performance is Compromised by Work is equal to the percentage of the population of all Students who Treat Academics like a Job. Thus, I am 95% confident that the percentage of all Students who Treat Academics like a Job is between –23.75% and 2.92% which is equal to the percentage of all Students who believe School Performance is Compromised by Work.

 

Conclusion

 In this report, the sample did not provided evidence that the majority of all Flagler College students who believe that their school performance is compromised by work.  In fact, it was estimated that between 70.99%  and 82.35%  of all Flagler College students treat academics like a job. Furthermore, it was found that there is not statistical evidence that students who believe that that their education is compromised by work treat academics like a job. It is estimated that between -23.75% and 2.92%  more of Flagler College students that believe their education is compromised by work  that treat academics like a job than all other Flagler College students. This is considered to us to be a natural association. 

Data set 1. Flagler College Students and Work - Adams, Omega;   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82633">Phase Three: Flagler College Students and Work Fall 2018 </A>

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