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Created: Dec 6, 2018
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Recycling PHASE 3
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Introduction:

During the first phase of this project, the recycling habits of 150 Flagler College students from the fall semester of 2018 was explored. In the second phase, the same sample of 150 students was divided into two smaller samples which were referred to as the Reusable Students and the Disposable Students. The term “Reusable Students” defined the sample of those Flagler College students who use reusable bags on a regular basis and the term “Disposable Students” defined the sample of those Flagler college students who do not use reusable bags on a regular basis. There are 65 Reusable Students and 85 Disposable Students sample. A pie chart representing the two samples is displayed below.


Result 1: Reusable vs. Disposable Bag Users

Result 1: Pie Chart With Data Reusable Bag Users vs. Disposable Bag Users   [Info]
Right click to copy

 

On this phase of the report, the students’ opinions about the difficulty of recycling on campus will be observed.

First, it will be determined if the sample results indicate that the majority of the population of all Flagler College students feel that it is difficult to recycle on campus through methods of statistical inferences. The statisticians will conduct a hypothesis test to find statistical evidence of the majority. After this hypothesis is created, a confidence interval will then be produced in order to estimate a percentage of the population of Flagler College students who feel that it is difficult to recycle on campus.

 

Second, the sample results will be used to determine if the opinion of the population of all Reusable Students and the population of all Disposable Students at Flagler College has a statistically significant difference of opinion regarding the difficulty of recycling on the Flagler College campus. Moreover, a hypothesis tests will be used to find this statistical evidence of the difference and then a confidence interval will be produced to estimate the difference in the percentage of the population of Reusable Students and Disposable Students who find recycling on campus to be difficult.


Hypothesis Test #1 – A Claim of Majority

Out of the 150 students surveyed, 89 reported that recycling on campus was difficult. The majority, 59.33%, of the Flagler students sampled reported that recycling on campus is hard. These sample results will be used to test the claim that the majority of the population of Flagler College students view social media as a distraction at a level of significance of 0.05. The pie chart for the data is displayed below.


Result 2: Difficulty to Recycle on Campus

Result 2: Pie Chart With Data flagler accessibility   [Info]
Right click to copy

 

Hypothesize

Null: Fifty percent of all Flagler College students believe that it is difficult to recycle on campus.

Alternate: More than 50% of all Flagler College students believe that it is difficult to recycle on campus.

Based on the alternate hypothesis, this is a right-sided test.


Prepare

  1. Random Sample - The sample may not be random due to the fact that the students surveyed were all taking Statistics classes. However, for the purpose of this project, we will proceed and assume that this sample is random.

  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. Flagler College has a population size of about 2500 students, which means that these samples should be representative of the population.

  4. Independence within Sample - Yes, the students each responded to the surveys individually which means that each sample was independent of one another.

 

Compute


Result 3: One sample hypothesis test

Result 3: One sample proportion summary hypothesis test 1   [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
p891500.593333330.0408248292.28619040.0111

 

Interpret

Since the p-value (0.0111) is less than the significance level of 0.05, the null hypothesis must be rejected. This means that there is significant evidence to claim that the majority of Flagler College students believe that is difficult to recycle on the college campus.


Confidence Interval #1 - Estimating the Population Proportion

The hypothesis test gives plenty of evidence to suggest that the majority of all Flagler College students feel that it is difficult to recycle on campus. Due to these results, a confidence interval will be created to estimate the percent of the population of all Flagler College students that believe it is difficult to recycle on campus. Since a one-tailed test with a significance level of 0.05 was run, a 90% confidence interval will be used.


Prepare

  1. Random Sample with Independent Observations - The sample may not be random due to the fact that the students surveyed were all taking Statistics classes. However, for the purpose of this project, we will proceed and assume that this sample is random. However, the students each responded to the surveys individually which means that each sample was independent of one another.

  2. Large Sample - Since n*phat = (150)(0.59333333) = 88.99 > 10 and n*(1 - phat) = (150)(1- 0.59333333) = (150)(.40666667) = 61 > 10, the sample is large.

  3. Big Population - Since 10n = (10)(150) = 1500 < 2500, the population is big. This is because Flagler College has a population size that is around 2500 students.


Compute

 

Result 4: One sample confidence interval

Result 4: One sample proportion summary confidence interval 1   [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
p891500.593333330.0401072640.527362760.65930391


Interpret

 

We are 90% confident that between 52.77% and 65.93% of all Flagler College students find that it is difficult to recycle on the Flagler College campus. Since the results are above 50%, this is undoubtedly the majority of all Flagler College students.


Hypothesis Test #2 – A Claim of the Difference Between Two Population Proportions

The contingency table created compares the opinions of the Reusable Students and the Disposable Students in relation to the difficulty to recycle on campus. 50 of the 85 Disposable Students felt that it was hard to recycle on campus and 39 of the 65 of the Reusable Students found that is was easy to recycle on campus. That is 58.8% (50 students out of 85) of the Disposable Students felt that it was difficult to recycle on campus, while 60% (39 students out of 65) of the reusable students felt that it was difficult to recycle on campus.  With slightly more than .01% difference in the percentage, the sample gives us no reason to believe that the population of Disposable students at Flagler and the population of Reusable students at Flagler differ in their opinion that it is hard to recycle on campus.


Result 5: Reusable Bags vs. Difficulty to Recycle

Result 5: Contingency table (with data) 3   [Info]

Contingency table results:


Rows: Use of Reusable Bags
Columns: Level of Difficulty for Recycling on Campus
No, HardYes, EasyTotal
No503585
Yes392665
Total8961150

Chi-Square test:


StatisticDFValueP-value
Chi-square10.0211283630.8844

 

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 Reusable Students at Flagler College and the proportion of the population of Disposable Students at Flagler College who feel that recycling on Flagler campus is difficult.

Alternate: There is a difference in the proportion of the population of Reusable Students at Flagler College and the proportion of the population of Disposable Students at Flagler College who feel that recycling on Flagler campus is different.

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) = (35 + 26)/(85 + 65) = 120/150 = 0.8

Sample One (Disposable Students): Since n1*p-hat = (85)(0.8) = 68 > 10 and

n1*(1 - p-hat) = (85)(1 – 0.8) = (85)(0.2) = 23.2 > 17, sample one is larger than 10.

Sample Two (Reusable Students): Since n2*p-hat = (65)(0.8) = 52 > 10 and

n2*(1 - p-hat) = (65)(1 – 0.8) = (65)(0.2) = 13 > 10, sample two is larger than 10.

2. Random Samples – Again, the samples are probably not random (but we hope they are representative of our study).  However, to proceed, we will assume they are 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 – Yes, there is no relationship between the Social Students and the Unsocial Students.


Compute

Result 6: Two sample summary stats

Result 6: Two sample proportion summary hypothesis test 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 - p2358526650.0117647060.0809371950.145355990.8844

 


Interpret
Since the p-value = 0.884 is greater than the level of significance of 0.05, the null hypothesis will not be rejected.  Therefore, there is not enough sufficient evidence to show that a difference exists in the proportion of the population of Reusable Students at Flagler College and the proportion of the population of Disposable Students at Flagler College who feel recycling on Flagler campus is difficult.


 

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

The hypothesis test did not give us enough sufficient evidence that there is a significant difference in the opinion that recycling on Flagler campus is difficult between the population of Reusable Students at Flagler College and the population of Disposable Students at Flagler College. Therefore, a confidence interval will be created to confirm that the 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. Also, yes, the student responses were taken in a way that their responses were independent of each other.

2. Large Samples

Sample One (Disposable Students): Since n1*p-hat1 = (85)(0.412) = 35.02> 10 and

n1*(1 - p-hat1) = (85)(1 – 0.412) = (85)(0.588) = 49.98 > 10, sample one is larger than 10.

Sample Two (Reusable Students): Since n2*p-hat2 = (65)(0.4) = 26 > 10 and

n2*(1 - p-hat2) = (65)(1 – 0.4) = (65)(0.6) = 39 > 10, sample two is larger than 10.

3. Big Populations – Recall, Flagler College has a population of appropriately 2500 students.  Since we are unsure what overall percentage of the students are or are not affected socially by social media, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Reusable Students and (0.50)(2500) = 1250 students who are Disposable Students in the population.

Population One (Disposable Students): Since 10n1 = (10)(85) = 850 < 1250, population one is big.

Population Two (Reusable Students): Since 10n2 = (10)(65) = 650 < 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 7: Two sample confidence interval

Result 7: Two sample proportion summary confidence interval 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 - p2358526650.0117647060.080881954-0.146761010.17029042




Conclusion

Society is changing in an attempt to become more environmentally conscious and realizing the havoc that plastic can have on the natural world.  In this report, our sample provided evidence that the majority of all Flagler College students find recycling on campus to be difficult. In fact, it was estimated that between 52.77% and 65.93% of all Flagler College students find that it is difficult to recycle on campus.  Furthermore, it was found that there is statistical evidence that those students who feel we don’t recycle enough on campus also used plastic bags instead of reusable.  It was estimated that between  -14.68% and 17.03% more of all Flagler College students felt that it was difficult to recycle on campus used plastic bags.  This is a strange association to me and makes me feel as though the recycling program at Flagler must be practically nonexistent in order for students who use plastic bags to also notice that we don’t have a good enough recycling program.

 

The underlying purpose of recycling and using reusable bags is to help the environment.  Hence, it is interesting that the majority of students don’t think we have a good enough recycling program, though they don’t even seem to use reusable bags themselves.  Maybe a better recycling program at Flagler would encourage students to become more environmentally cautious and create a positive difference in the world around them. It may help students feel that they can make a difference in our currently destructive plastics situation.  Although enforcing such a policy that would be difficult due to the cost of obtaining enough recycling bins, it is something to consider. On the other hand, using any kind of bin with a sign on it that says recycling, whether it be a crate, rubbish bin, or a brown paper bag, might allow students to recycle openly without having to pay more bins, which we could use to contribute to our currently small recycling program. The environment is changing as we add more plastics and other pollutants to it, and it is making people around the world sick and killing off food supplies and naturally beautiful scenery, so doing our part to recycle might prove to be more popular than our college campus currently thinks it to be.


Data set 1. Jennifer_Emmaline_Eve_FCStudents and Recycling   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82753">Recycling PHASE 3</A>

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