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PHASE THREE: The Importance of Education to Flagler College Students
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PHASE THREE: The Importance of Education to Flagler College Students


On page first phase of this project, The Importance of an Education with a sample of 150 Flagler College Students from the 2019 spring semester was what we explored. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as the Importance of GPA and Non-importance of GPA. The term “Importance” defined the sample of those Flagler College students who do not think GPA is important was used with the term “Non-importance”. There are 63 students that think GPA is not as important and 87 said GPA is important. A bar chart representing the two samples is presented below.

 

Result 1: Bar Plot- Importance and Non-impotence of GPA pt   [Info]
Right click to copy

 

 


On this phase report, attention will be given to students’ opinions about the importance and non-importance of GPA for their future careers and opportunities in the workforce.


First, methods of statistical inference will be used to determine if the sample results indicate that the majority of the population of Flagler College Students feel that GPA is important to their 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 GPA is not important for education.


Second, the sample results will also be used to determine if the opinion of the population all the students who think GPA is importance and the population of  all students who think GPA is not important at Flagler College have a statistically significant difference in opinion regarding going to graduate school. Again the Hypothesis test will be run to find statistical evidence of a difference and then the confidence interval will be created to estimate the difference.


Hypothesis Test #1 A Claim of Majority


In the sample of 150 students, 87 reported that GPA is important to get into Grad School. That is the majority 58%, of the students sampled expressed that GPA is important to get into Grad School. These sample results will be used to test the claim that the majority of the population of Flagler College students view Grad School as an important incentive for their GPA. The level of significance of 0.05 . A pie chart if the data is given below.

Result 2: GPA   [Info]
Right click to copy

 


Hypothesize

Null: Fifty percent of all Flagler College students believe that GPA is important to go to Grad School.

Alternative: More than 50% of all Flagler students believe that GPA is important to get into Grad School.


Prepare

  1. Random Sample with Independent Observation- Again probably not (but we hope it is representative). However, to proceed we will assume it is. Furthermore, yes, the students responses were taken in such a way that their responses were independent of each other.

  2. Large Sample- Since n” phat = (150)(.58) = 87 > 10 and n” (1-phat) = (150)(1-0.58) = (150)(.42) = 63 >10, the sample is large.

  3. Big Population- since 10n= (10)(150)= 1500 < 2500, the population is big.

  4. Independence Within Sample- yes the the student responses were taken is such a way that their responses were independent of each other.  

Compute

 

Result 3: One sample proportion summary hypothesis test - Importance of GPA   [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
p871500.580.0408248291.95959180.025

Interpret

Since the p-value ( 0.025) is less than the level of the significance of .05 the null hypothesis must be rejected. Therefore there is sufficient evidence to support that more than 50% of Flagler College students think GPA is important to get into grad school.

Confidence Interval# 1 -Estimating the population proportion.

The hypothesis test gives sufficient evidence to support that more than 50% of college students think that GPA is important to go to grad School. Therefore a confidence interval will be created to estimate the percent of the population of Flagler College students who think that GPA is Important to a Grad school.

Prepare

  1. Random Samples with independent Variables- yes the student responses were taken in such a way that their responses were random and independent of each other.

  2. Large sample- n*phat= (150)(.58) =87>10 and n*(1-phat) = (150)(.42)=63>10, The sample is large.

  3. Big population. Since 10n =(10)(150)= 1500

Compute

 

Result 4: One sample proportion summary confidence interval - Importance of GPA   [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
p871500.580.0402988830.513714240.64628576

Interpret-

We are 90% confidence that between 51.4% and 64.2% of all Flagler College students believe that GPA is important for grad school.

Hypothesis Test #2- A Claim of difference between two population proportions.

A contingency table was used to compare the opinions of students that plan on going to grad school and students that do not plan on going to grad school regarding their opinion on whether or not GPA is important for Grad school. Of the 63 Students that think GPA is not  important for Grad school 34 plan to attend grad school and of the 87 students who do think that GPA is important 65 plan on attending graduate school. That is 53% of the students that think GPA is not important for grad school plan on attending and 74% of the students that do think GPA is important for grad plan on attending. With a 21% difference in these percentages, the sample gives some reason to believe that the population of Flagler students that Do believe GPA is important for Grad School and the Population of Flagler students that do not believe GPA is important for grad school differ on whether or not they are attending grad school.

 

Result 6: Two sample proportion summary hypothesis test - HT #2   [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 - p234636587-0.20744390.078365905-2.64711930.0081

 

A hypothesis test will be used to determine if this difference is statistically significant for the population of students at flagler college.

Hypothesize

Null: There is no difference in the proportion of the population of Flagler Students that believe GPA is important for grad school and Flagler students that do not think GPA is important for grad school who plan on attending grad school.

Alternate:  There is a difference in the proportion of the population of Flagler Students that believe GPA is important for grad school and Flagler students that do not think GPA is important for grad school who plan on attending grad school.

Prepare:

  1.   Large Samples – It is found that the pooled sample proportion is

p-hat = (x1 + x2)/(n1 + n2) = (34 + 65)/(63 + 87) = 99/150 = 0.66

Sample One (Social Students): Since n1*p-hat = (63)(0.66) = 41.6 > 10 and

n1*(1 - p-hat) = (63)(1 – 0.66) = (63)(0.34) = 23.31 > 10, sample one is large.

Sample Two (Unsocial Students): Since n2*p-hat = (87)(0.66) = 57.4 > 10 and

n2*(1 - p-hat) = (87)(1 – 0.66) = (63)(0.34) = 21.4 > 10, sample two is large.

    2. Random Samples: The samples were random

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: The two samples are independent from one another.

Compute

Result 6: Two sample proportion summary hypothesis test - HT #2   [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 - p234636587-0.20744390.078365905-2.64711930.0081

 

 

Interpret

Since the p – value = 0.0081 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 the Students at Flagler that believe GPA is important and the population proportion of students at Flagler College that believe Gpa is important for Grad School on whether or not they plan to attend.

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 of the population of students that think Gpa is important for Grad school  between the population of students at flagler college that do not believe GPA is important for Grad School. 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 Sample with Independent Observations: yes, the student responses were taken in such a way that their responses were independent of each other.

  2. Large Samples-

         Sample One: Since n1*p-hat1 = (63)(0.66) = 41 > 10 and

n1*(1 - p-hat1) = (63)(1 – 0.66) = (63)(0.34) = 21 > 10, sample one is large.

         Sample two- Since n2*p-hat2 = (87)(0.66) = 59 > 10 and

n2*(1 - p-hat2) = (87)(1 – 0.66) = (63)(0.34) = 10 > 10, sample two is large.

3. The Samples are random.

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

5. Independence between samples- Yes the samples are independent from one another.

Compute

 

Result 7: Two sample proportion summary confidence interval - CI #2   [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 - p234636587-0.20744390.078197512-0.3607082-0.05417959

 

Interpret.

This confidence interval is completely negative; this indicates that the percentage of the population of all Flagler college students who think GPA is not important for Grad school is less than the percentage of the population of all Flagler college students who do not think GPA is important for grad school. Thus, I am 95% confident that the percentage of all Flagler college students who think that Gpa is important for Grad School adn plan on attending grad school is between 36% and 54% greater than the percentage of all Social Students who Plan on going to college. 

 

Conclusion

 

College students have opinions on whether GPA is of importance or of non-importance to an individual’s career. In this report, the sample provided evidence that the majority of FLagler College students find that GPA is important. In fact, it was estimated that between  42% and 58% of all FLagler College students find that college GPA is important. Furthermore, found that there was statistical evidence that those students who feel GPA is important would want to go to graduate school.


Result 5: Contingency table (with data) - GPA and Graduate School   [Info]

Contingency table results:


Rows: GPA
Columns: Graduate School
NoYesTotal
No293463
Yes226587
Total5199150

Chi-Square test:


StatisticDFValueP-value
Chi-square17.00724040.0081

Data set 1. Landry, Matthaei, and Byrne - Flagler College Stud   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=87121">PHASE THREE: The Importance of Education to Flagler College Students </A>

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