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Phase Three: Flagler College Students and Education
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Introduction 

 

On the first phase of this project, opinions about education from 150 students at Flagler College were examined. In the second phase, these opinions were split into two smaller categories; students who reported having A grades and students who reported earning B/C grades. The group who received A’s were termed simply “A Students” and those who earned lower grades were defined as “B/C Students”. There were 66 A Students and 84 B/C students sampled. A bar chart representing the two samples is presented below. 

 

 

Result 1: Bar Plot With Data   [Info]
Right click to copy

On this phase of the report, attention will be given to students’ opinions about the importance of education. 

First, methods of statistical inference will be used to determine if the sample results indicate that a majority of the population of all Flagler College students are interested in continuing their education in graduate school. A hypothesis test will first be run to find statistical evidence of a majority and then a confidence interval will be created to estimate the percentage of the population of Flagler College students who intend to go on to graduate school. 

Second, the sample results will also be used to determine if the opinion of the population of all A Students and the population of all B/C Students have a statistically significant difference of opinion regarding the desire to continue education through graduate school. 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 A Students and B/C Students who intend to go on to graduate school. 

 

Hypothesis Test #1-A Claim of Majority 

 

In the sample of 150 students, 104 intended to go on to graduate school while 46 students did not. That is, the majority, 69.33% of the students sampled expressed that they planned to go on to graduate school. These sample results will be used to test the claim that the majority of the population of Flagler College students intended to go on to graduate school at a significance of 0.05. A pie chart for the data is given below. 

 

Result 2: Pie Chart With Data Displaying the Type of Students   [Info]
Right click to copy

 

Hypothesize: 

 

Null: Fifty percent of all Flagler College students intend to go on to graduate school. 

 

Alternate: More than 50% of all Flagler College students intend to go on to graduate school. 

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 - Graduate School   [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
p1041500.693333330.0408248294.7356802<0.0001

Interpret  

Since the p-value (<.0001) is lower than .05, there is insufficient evidence to accept the claim that fifty percent of all Flagler College students intend to go on to graduate school. 

 

Confidence Interval #1 – Estimating the Population Proportion 

 

The hypothesis test (H0: P=.50)  gives insufficient evidence that the majority of all Flagler College students intend to go on to graduate school. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that social media is a distraction to their day. 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)(0.6933) = 104 > 10 and n*(1 – phat) = (150)(1 – 0.6933) = (150)(0.3067) = 46 > 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 - Graduate School   [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
p1041500.693333330.0376494550.631405490.75526118


 

We are 90% confident that between 62.62% and 76.04% of all Flagler College students intend to go on to graduate school. This is greater than the majority of all Flagler College students.

 

A hypothesis test will be used to determine if this difference is statistically significant for the population of A and B/C type students.  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 between A students and B/C Students who have the intention of going to graduate school. 

 

Alternate: There is a difference in the proportion of the population between A students and B/C Students who have the intention of going to graduate school. 

 

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) = (45 + 59)/(66 + 84) = 104/150 = 0.6933 

 

Sample One (A Students): Since n1*p-hat = (66)(0.6933) = 45.8> 10 and 

 

n1*(1 - p-hat) = (66)(1 – 0.6933) = (66)(0.3067) = 20.2> 10, sample one is large. 

 

Sample Two (B/C Students): Since n2*p-hat = (84)(0.6933) = 58.2 > 10 and 

 

n2*(1 - p-hat) = (84)(1 – 0.6933) = (84)(0.3067) = 25.8> 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 A Students and B/C Students.  

 

Compute 

 

Result 5: Contingency Table for Student Types and Grad School   [Info]
Contingency table results:
Rows: Type of Student
Columns: Graduate School
NoYesTotal
A Student214566
B/C Student255984
Total46104150

Chi-Square test:
StatisticDFValueP-value
Chi-square10.073499870.7863

Since the p-value = 0.7863 is more than the level of significance of 0.05, the null hypothesis cannot be rejected.  Therefore, there is not sufficient evidence that there exists a difference in the proportion of the population between A students and B/C Students who have the intention of going to graduate school. 

 

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

 

The hypothesis test did not provide sufficient evidence that there is a significant difference in the population between A students and B/C Students who have the intention of going to graduate school. Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions can 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 (A students): Since n1*p-hat1 = (66) (0.683) = 45 > 10 and 

 

n1*(1 - p-hat1) = (66)(1 – 0.683) = (66)(0.317) = 21 > 10, sample one is large. 

 

Sample Two (B/C Students): Since n2*p-hat2 = (84)(0.702) = 59 > 10 and 

 

n2*(1 - p-hat2) = (84)(1 – 0.702) = (84)(0.298) = 25 > 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 that do or do not intend on going to graduate school, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are A students and (0.50)(2500) = 1250 students who are B/C Students in the population. 

 

Population One (A students): Since 10n1 = (10)(66) = 660 < 1250, population one is big.  

 

Population Two (B/C Students): Since 10n2 = (10)(84) = 840 < 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 6: Two sample proportion summary hypothesis test - HT #2 (Two Sample)   [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 - p245665984-0.0205627710.075846989-0.271108590.7863

    

This 90% confidence interval contains zero; this indicates that there is no difference between the proportion of all Flagler College A Students and B/C students who intend on going to graduate school.  Thus, there is not sufficient evidence to conclude that the proportion of A students in the population who intend to go to graduate school is greater than the proportion B/C students who intend to go to graduate school.  

 

Result 7: Two sample proportion summary confidence interval   [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 - p245665984-0.0205627710.075997348-0.145567280.10444174

 

Interpret:

This confidence interval includes zero so the population proportions may be equal because if P1-P2=0, then P1=p2. We are 90% confident that the percentage of all A Students who intend to go to graduate school is between -.146 and .104. We cannot make many conclussions based on this data. 

Conclusion 
 

The prospect of further pursuing education is one that is predominantly embedded into students and increasingly becomes a very relevant subject to tackle. In this report, the sample provided evidence that the majority of all Flagler College students have the prospect of attending graduate school. The approximate value of comparison between A students and B/C showed that there was no difference in the intention of going to graduate between the two samples. To add more, it was estimated that between 62.62% and 76.04% of all Flagler College students intend to go on to graduate school rather than not. The results indicate the imperative that students have in their academic careers and further explore that field. We find ourselves more eager to learn and improve.

Educational institutions fundamentally exist as a form of guidance. Although it seems conceivable at first that most students would be content with a bachelor level of qualification or understanding of a field. Rather, it seems that the census lies with the prospect of a mastery level of that subject is often more preferable. We can interpret our results from these samples cut down essentially in two ways; students view graduate school as a necessity in the process of obtaining a sustainable job or a necessity in the pursuit of better understanding their vocation in life. 

Data set 1. Flagler College Students and The Importance of an   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82811">Phase Three: Flagler College Students and Education</A>

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