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 Nonimportance 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 “Nonimportance”. 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.
On this phase report, attention will be given to students’ opinions about the importance and nonimportance 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.
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

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.

Large Sample Since n” phat = (150)(.58) = 87 > 10 and n” (1phat) = (150)(10.58) = (150)(.42) = 63 >10, the sample is large.

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

Independence Within Sample yes the the student responses were taken is such a way that their responses were independent of each other.
Compute
One sample proportion summary hypothesis test:p : Proportion of successes H_{0} : p = 0.5 H_{A} : p > 0.5 Hypothesis test results:

Interpret
Since the pvalue ( 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

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.

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

Big population. Since 10n =(10)(150)= 1500
Compute
One sample proportion summary confidence interval:p : Proportion of successes Method: StandardWald 90% confidence interval results:

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.
Two sample proportion summary hypothesis test:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions H_{0} : p_{1}  p_{2} = 0 H_{A} : p_{1}  p_{2} ≠ 0 Hypothesis test results:

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:

Large Samples – It is found that the pooled sample proportion is
phat = (x1 + x2)/(n1 + n2) = (34 + 65)/(63 + 87) = 99/150 = 0.66
Sample One (Social Students): Since n1*phat = (63)(0.66) = 41.6 > 10 and
n1*(1  phat) = (63)(1 – 0.66) = (63)(0.34) = 23.31 > 10, sample one is large.
Sample Two (Unsocial Students): Since n2*phat = (87)(0.66) = 57.4 > 10 and
n2*(1  phat) = (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
Two sample proportion summary hypothesis test:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions H_{0} : p_{1}  p_{2} = 0 H_{A} : p_{1}  p_{2} ≠ 0 Hypothesis test results:

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

Random Sample with Independent Observations: yes, the student responses were taken in such a way that their responses were independent of each other.

Large Samples
Sample One: Since n1*phat1 = (63)(0.66) = 41 > 10 and
n1*(1  phat1) = (63)(1 – 0.66) = (63)(0.34) = 21 > 10, sample one is large.
Sample two Since n2*phat2 = (87)(0.66) = 59 > 10 and
n2*(1  phat2) = (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
Two sample proportion summary confidence interval:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions 95% confidence interval results:

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 nonimportance 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.
Contingency table results:Rows: GPA Columns: Graduate School
ChiSquare test:

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