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PHASE THREE: Flagler College Students and the Plus-Minus Grading System Fall 2018
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PHASE THREE: Flagler College Students and the Plus-Minus Grading System Fall 2018

A+ Included/profit


Introduction:

Throughout this project, the first of the three phases sampled 150 students at Flagler College during Fall 2018 about whether they think the college should keep the plus-minus grading system. Phase two splits the sample into two groups; the students who believe they will profit from the plus-minus grading system and the students who do not believe they will profit. The two new samples were named “students who profit” and “students who don’t profit.” This final phase took a look at if students believe there should be an A+ grade added to the already plus-minus grading system at Flagler college. Of the 150 students sampled, 120 of them believe that yes, the plus-minus grading system should include an A+ and would be beneficial, leaving 30 students who do not. A pie chart representing this data is below.


Result 1- Students Who Profit From the Plus-Minus Grading System and Students Who Don’t:

 

This phase of the report focuses on the sample of Flagler college students’ opinions as to whether they profit from the plus-minus grading system or not. Through methods of statistical inference we will determine if the sample results show that a majority of Flagler college students feel that they profit from the plus-minus grading system. We will run a hypothesis test to find evidence for a majority and then create a confidence to interval to estimate the percentage of Flagler College students who profit from the plus-minus grading system.


Then we will use the sample results to test whether students who want A+ included in the grading system and students who don’t have a statistically significant difference of opinion regarding if they profit from the plus-minus grading system. We will run a hypothesis test to find evidence of a statistically significant difference and then use a confidence interval to estimate the percentage of the population of students that want to keep A+ and students that don’t who profit from the plus-minus grading system.


Hypothesis Test #1- A Claim of Majority

In the sample of 150 students, 120, also the majority of 80%, said they wanted to keep A+ in the plus-minus grading system. The results from this sample will be used to test the claim that the majority of the population of Flagler College Students want to keep A+ in the grading system with a significance level of 0.05. A pie chart of the data is given below

 


Hypothesize

Null: Fifty percent of all Flagler College students want A+ included in the grading system.

Alternate: More than 50% of all Flagler College students want A+ in the grading system

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, the sample is large.

3. Big Population – Since 10n = (10)(150) = 1500 < the population.  Flagler College has a population of appropriately 2500 students. The population is big.

4. Independence within Sample – The students were surveyed in a way so that there responses were indepent.

Compute

 

Interpret

We must reject the null hypothesis since the p-value (

 

Confidence Interval #1- Estimating the Population Proportion

The hypothesis test gave us sufficient evidence to that the majority of all Flagler College students want to keep A+ in the plus-minus grading system. So we will create a confidence interval to estimate the percent of the population of all Flagler College students who want to keep A+ in the grading system. Since we ran a one tailed test with a significance level of 0.05, we will create a 90% confidence interval.

Prepare

1. Random Sample with Independent Observations – Again, probably not. However, to proceed, we will assume it is.  And yes, the students were surveyed in such a way that there responses were indepent.

2. Large Sample – Since n*phat = (150)(0.8) = 120 > 10 and n*(1 – phat) = (150)(1 –0.8) = (150)(0.2) = 30 > 10, the sample is large.

3. Big Population – Since 10n = (10)(150) = 1500 < the population.  Flagler College has a population of appropriately 2500 students.The population is big.

Compute

 

Interpret

We are 90% confident that between 74.6% and 85.4% of all Flagler College students want to keep A+ in the plus-minus grading system. This is the majority of all Flagler College students.




Hypothesis Test #2 – A Claim of the Difference between two Population Proportions


In order to compare the students who profit and the students who don’t profit in regards to including the A+ in the grading system, we created a contingency table as seen below. Out of the 56 students who don’t profit, 38 students believed the A+ should included in the grading system, and out of the 94 students who profit, 82 believed the A+ should also be included. That comes out to being 67.9% (38 out of 56) of students who don’t profit believe the A+ should be included and 87.2% (82 out of 94) of students who profit believe the A+ should be included. Because the differing percentage of the two groups (19.3% difference), there is evidence to believe that between the population of students who profit and the population of students who don’t profit have a different opinion of whether the A+ should be included into the grading system.

Using a significance level of .5, we will use a hypothesis test to determine if this difference in percentage holds true to the entire population of Flagler students.


Hypothesize


Null: There is no difference in proportions between the students who profit and the students who don’t profit who believe that the A+ should be included in the grading system.
Alternate: There is a difference in proportions between the students who profit and the students who don’t profit who believe that the A+ should be included in the grading system.
Because of the alternate hypothesis, this is a two-tailed test.


Prepare:
1.Large Samples- surveyed sample proportion is

p-hat = (x1 + x2)/(n1 + n2) = (38 + 82)/(56 + 94) = 120/150 = 0.8

Sample One (Students who don’t profit): Since n1*p-hat = (56)(0.8) = 44.8 > 10 and

n1*(1 - p-hat) = (56)(1 – 0.8) = (81)(0.2) = 16.2 > 10, sample one is large.

Sample Two (Students who do profit): Since n2*p-hat = (94)(0.8) = 75.2 > 10 and

n2*(1 - p-hat) = (94)(1 – 0.8) = (94)(0.2) = 18.8 > 10, sample two is large.

2.Random Samples- Even though they are probably not random, for this test we will just say that they are.
3.Independent Samples- These are independent samples because of how the students were surveyed.
4.Independence Between Samples- There is independence between the samples of the students who profit and the students who don’t profit.

Compute


Interpret


After computing the two-sample hypothesis test, the table shows that the p-value (0.0041) is less than our significance level (0.5). Because of this, there is enough evidence to say that there is a difference between the proportion of the population of students who profit and the proportion of the population of students who don’t profit in regard to whether they believe the A+ should be included.


Confidence interval #2- Estimate the Difference between two Population Proportions


Because of the difference between the population of students who profit who believe the A+ should be included and the population of students who don’t profit who believe the A+ should be included, a confidence interval was created to show the difference and confirm that both populations cannot be equal to each other. In this test, a 95% confidence was used because the test was two-tailed and a significance level of 0.5 was used.


Prepare:
1.Random Samples with Independent Observations- as stated above, while they are probably not random, we will say that the samples were random. As also stated above, the observations were independent.

2.Large Samples-

Sample One (Students Who Don’t Profit): Since n1*p-hat1 = (56)(0.679) = 38 > 10 and

n1*(1 - p-hat1) = (56)(1 – 0.679) = (56)(0.321) = 18 > 10, sample one is large.

Sample Two (Students Who Profit): Since n2*p-hat2 = (94)(0.872) = 82 > 10 and

n2*(1 - p-hat2) = (94)(1 – 0.872) = (94)(0.128) = 12 > 10, sample two is large.

3.Big Populations- Even though we know that Flagler College has a population of about 2500 students, we cannot accurately state whether any of the students believe that the A+ should be included or not included. For this test however, we will just say that 50% believe the A+ should be included and that 50% believe the A+ shouldn’t be included. Therefore there are 1250 (.5 x 2500) who believe the A+ should be included and 1250 (.5 x 2500) who believe the A+ should not be included.

Population One (Students Who Don’t Profit): Since 10n1 = (10)(56) = 560 < 1250, population one is big.

Population Two (Students Who Do Profit): Since 10n2 = (10)(94) = 940 < 1250, population two is big.
4.Independent Samples- Due to how the students were surveyed, they are independent samples.

Compute


Interpret
The upper and lower limits of the confidence interval are both negative which means that the percentage of the population of the students who don’t profit who believe the A+ should be included is less than the percentage of the population of students who do profit who believe the A+ should be included, Therefore we can say that we are 95% confident that the percentage of students who profit who believe the A+ should be included is between 5.4% and 28.7% greater than the percentage of students who don’t profit who believe the A+ should be included.

Conclusion

In this report the sample provided evidence that the majority (between 74.6% and 85.4%)  of all Flagler college students want to keep A+ in the plus-minus grading system. Furthermore, we found statistical evidence supporting that a greater percentage of the students that profit from the plus-minus grading system believe A+ should be kept in the grading system than of the students who don’t profit.  Of students who profit those who believe the A+ should be included is between 5.4% and 28.7% greater than the percentage of students who don’t profit who believe the A+ should be included.

Result 1: Profit from Plus-Minus Grading System Fall 2018   [Info]
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Result 2: A+ Included   [Info]
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Result 3: One sample proportion summary hypothesis test- A+ Included   [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
p1201500.80.0408248297.3484692<0.0001

Result 4: One sample proportion summary confidence interval-A+ Included   [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
p1201500.80.0326598630.746279310.85372069

Result 5: Contingency Table - Those Who Profit VS Those Included   [Info]
Contingency table results:
Rows: Profit from Plus-Minus Grades
Columns: A+
NoYesTotal
No183856
Yes128294
Total30120150

Chi-Square test:
StatisticDFValueP-value
Chi-square18.23518240.0041

Result 6: Two sample proportion summary hypothesis test- A+ Included vs. Profit   [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 - p238568294-0.1937690.06752237-2.86970070.0041

Data set 1. Maravilla, Mirabella, Morrissey, Weatherly   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82771">PHASE THREE: Flagler College Students and the Plus-Minus Grading System Fall 2018</A>

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