PHASE THREE: Flagler College Students and Plus/Minus Grades in Fall 2018
Introduction:
On the first phase of this project, the survey results of plus minus grades and general student information was explored. The survey results were from a sample of 150 Flagler College students from fall semester 2018. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as female Flagler college students surveyed and male Flagler college students surveyed. The term F defines Female Flagler college students and the term M defines Male Flagler college students. There are 68% F Students and 32% M Students. There are 102 Female Students and 48 Male Students sampled. A bar chart representing the two samples is presented below.
On this phase of the report, attention will be given to students’ opinions about whether or not they feel students GPAs profit from the plus minus grading systems>
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 students GPAs profit from the plus minus grading system. 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 students GPAs profit from the plus minus grading system.
Second, the sample results will also be used to determine if the opinion of the population of all female Flagler college students surveyed and male Flagler college students surveyed have a statistically significant difference of opinion regarding the plus minus grading system. 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 female students and male students who find the plus minus grading system boosts students GPAs.
Hypothesis Test #1 – A Claim of Majority
In the sample of 150 students, 102 reported that they feel students GPAs profit from the plus minus grading system. That is, the majority, 69.33%, of the students sampled expressed that social media is a distraction. These sample results will be used to test the claim that the majority of the population of Flagler College students view the plus minus grading system as profitable to GPAs at a level of significance of 0.05 A pie chart of the data is given below.
Hypothesize
Null: Fifty percent of all Flagler College students believe that students GPAs profit from the plus minus grading system at Flagler.
Alternate: More than 50% of all Flagler College students believe that students GPAs profit from the plus minus grading system at Flagler.
Based on the alternate hypothesis, this is a rightsided test.
Prepare
1. Random Sample – It is highly unlikley that this is a random sample (but we hope it is representative). However, to proceed, we will assume it is.
2. Large Sample – Since np_{0} = (150) (0.50) = 75 > 10 and n(1p_{0}) = (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. 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
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 (<0.0001) 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 feel that the plus minus grading system increases students GPAs.
Confidence Interval #1 – Estimating the Population Proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that the plus minus grading system increases students GPAs. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that the plus minus grading system increases students GPAs. 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) = 103.995 > 10 and n*(1 – phat) = (150)(1 – 69.33) = (150)(0.3067) = 46.005 > 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
One sample proportion summary confidence interval:p : Proportion of successes Method: StandardWald 90% confidence interval results:

Interpret
We are 90% confident that between 63.1% and 75.5% of all Flagler College students find that GPAs profit from the plus minus grading system. 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 female students and the male students regarding whether or not GPAs profit from the plus minus grading system. Of the 102 female students, 68 felt GPAs profit from the plus minus grading system and of the 48 male students, 36 felt social media was a distraction. That is, 66.7% (68 students out of 102) of the female students felt GPAs profit from the plus minus grading system and 75% (36 students out of the 48 students) of the male students felt GPAs profit from the plus minus grading system. With an approximately 8.3% difference in these percentages, the sample gives some reason to believe that the population of male students at Flagler College and the population of female students at Flagler College differ in their opinion that GPAs profit from the plus minus grading system.
Contingency table results:
Rows: Gender Columns: Profit from PlusMinus Grades
ChiSquare test:

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 female students at Flagler College and the proportion of the population of male students at Flagler College who feel GPAs profit from the plus minus grading system.
Alternate: There is a difference in the proportion of the population of female students at Flagler College and the proportion of the population of male students at Flagler College who feel GPAs profit from the plus minus grading system.
Based on the alternate hypothesis, this is a two tailed test.
Prepare:
1. Large Samples – It is found that the pooled sample proportion is
phat = (x_{1} + x_{2})/(n_{1} + n_{2}) = (68 + 36)/(102 + 48) = 104/150 = 0.6933
Sample One (female students): Since n_{1}*phat = (68)(0.6933) = 47.14 > 10 and
n_{1}*(1  phat) = (102)(1 – 0.6933) = (102)(0.3067) = 31.2834 > 10, sample one is large.
Sample Two (male students): Since n_{2}*phat = (48)(0.6933) = 33.2784 > 10 and
n_{2}*(1  phat) = (48)(1 – 0.6933) = (48)(0.3067) = 14.7216 > 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 Social Students and the Unsocial Students.
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 = 0.3018 is greater than the level of significance of 0.05, the null hypothesis will not be rejected. Therefore, there is not sufficient evidence that there exists a difference in the proportion of the population of female students at Flagler College and the proportion of the population of male students at Flagler College who feel GPAs profit from the plus minus grading system.
Confidence Interval #2 –Estimate the Difference between two Population Proportions
The hypothesis test did not give us sufficient evidence that there is a significant difference in the opinion that GPAs profit from the plus minus grading system between the population of male and female 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 (Female Students): Since n_{1}*phat_{1} = (102)(0.667) = 68.034 > 10 and
n_{1}*(1  phat_{1}) = (102)(1 – 0.667) = (102)(0.333) = 33 .966> 10, sample one is large.
Sample Two (Male Students): Since n_{2}*phat_{2} = (48)(0.75) = 36 > 10 and
n_{2}*(1  phat_{2}) = (48)(1 – 0.75) = (48)(0.25) = 12 > 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 do not believe the plus minus gradinging system profits GPAs, we will assume 50% are and 50% are not. Hence, there are approximately (0.50)(2500) = 1250 students who are female students and (0.50)(2500) = 1250 students who are male students in the population.
Population One (Female Students): Since 10n_{1} = (10)(102) = 1020 < 1250, population one is big.
Population Two (Male Students): Since 10n_{2} = (10)(48) = 480 < 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
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 half negative and half positive; this interval contains zero so it could be equal therfore there is no significant diference betwen gender and opinions on the plus minus grading system. I am 95% confident that the difference in the percentage of all Flagler College females and the percentage of Flagler College males who feel that students GPA's benifit from the plus minus grading system are between 23.6% as an lower limit and 7% as an upper limit. Since this confidence interval contains zero, there is a possibility that the percentage of all Flagler College males and females who believe that students GPAs benifit from the plus minus grading system could be equal. This certainly supports the results of the hypothisis test that there is no signifigant differences in the two population percentages.
Conclusion
The plus minus grading system affects every student at Flagler College, whether or not students believe there GPAs profit is a very important topic. In this report, the sample provided evidence that the majority of all Flagler College students find the plus minus grading system is boosted by GPA. In fact, it was estimated that between 63.1% and 75.5% of all Flagler College students find that GPAs profit from the plus minus grading system. Furthermore, It can be concluded that a majority of Flagler college students feel like their GPAs profit from the plus minus grading system. We are 95 percent confident that between 23.6% and 7% of F and M students of Flagler College feel students GPA's benifit from the plus minus grading system. The confidence interval contains zero, so there is a possibility that the percentage of all Flagler College males and females who believe that students GPAs benifit from the plus minus grading system could be equal. This is natural association to me. I feel like Flagler college would not institute a grading system that is not aimed at improving overall GPAs of student.
It is possible that some students do not understand the plus minus grading system. I would consider myself part of that group. That group may have given the school the benifit of the doubt and assumed they have their student best intrests at heart. That assumption would be that the school uses the plus minus grading system because it causes a boost in GPA for students. Other students unsure of the system may have just randomly guessed knowing the surveys would likley be a completion grade. There is really no conlusion to be drawn, because gender did not show a impact on the opinion, if the plus minus grading system profits students GPAs.
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