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Phase 3: Recycling
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PHASE THREE: Environmentally Friendly Habits of Students


Introduction:


On the first phase of this project, the environmentally friendly habits of students of a sample of 150 Flagler College students from fall semester 2018 were explored. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as those who use “Reusable Bags” and those who don’t use reusable bags labelled as “Non Reusable Bags”. There are 90 “No Reusable Bag” students and 60 “Reusable Bags”.  A bat chart representing the two samples is presented below.


Result 1: Reusable Bag and Non Reusable Bag Students

Result 1: Phase 3: Reusable bag bar graph   [Info]
Right click to copy


On this phase of the report, attention will be given to students’ opinions about the use of reusable bags.


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 do not use reusable bags while shopping. 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 reusable bags are not a priority when shopping.  


Second, the sample results will also be used to determine if the opinion of the population of all Reusable Bag students and Non Reusable Bags students have a statistically significant difference of opinion regarding the effect of using Reusable bags when shopping. 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 Reusable Bag students and Non Reusable Bag students who use reusable bags when shopping.



Hypothesis Test #1- A Claim of Majority


In the sample of 150 students, 91 reported that it is difficult to recycle on campus. That is, the majority, 60,67%, of the students sampled expressed that recycling is difficult on campus. These sample results will be used to test the claim that the majority of the population of Flagler College students believe that recycling is difficult on campus at a level of significance of 0.05  A pie chart of the data is given below.


Result 2: Pie Chart With Data- Recycling on Campus- Is it Difficult

Result 2: Phase 3: Correct pie graph   [Info]
Right click to copy


Hypothesize

    Null: Fifty percent of all Flagler College students believe that social media is a distraction to their day


     Alternate: More than 50% of all Flagler College students believe that social media is a distraction to their day.


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 are both true statements, 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.

 

    4. Independence within Sample – Yes, the student responses were taken in such a way that their responses were independent of each other.

 

Compute


Result 3: One sample proportion summary hypothesis test- Distraction

Result 3: Phase 3: Correct Hypothisis test   [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
p911500.606666670.0408248292.61278910.0045


Interpret


Since the p-value (<.0004 ) 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 it is difficult to recycle on campus.


Confidence Interval #1- Estimating the Population Proportion

 


The hypothesis test give sufficient evidence that the majority of all Flagler College students feel that recycling is difficult on campus. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that recycling on campus is difficult. Since a one tailed test with a level of significance of 0.05 was run, 90% confidence interval will be created.


Prepare

1. Random Sample with Independent Observations – 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 from each other.

           2. Large Sample- Since n*phat = (150)(0.60667) = 100.9  ³ 10 and n*(1 – phat) = (150)(1-0.6067) = (150)(0.3267) = 49 ³ 10, the sample is large.

           3. Big Population- Since 10n = (10)(150) = 1500 < 2500, the population is big. The population at Flagler College is roughly 2500.

 

       Compute


Result 4: Phase 3: Correct confidence interval   [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
p911500.606666670.039885020.541061650.67227169


Interpret

We are 90% confident that between 54.12% and 67.23% of all Flagler College students do not feel it is difficult to recycle on campus. 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 students that use reusable bags and those that find it difficult to recycle on campus. Of the 90 that do not use recyclable bags, 55 of them found hard to recycle on campus, and of the 60 students that did use recyclable bags, 36 thought that recycling on campus was hard. That is, 61.1% (55 students out of 90) of the students that do not use recyclable bags, who thought recycling on campus was hard, and 60% (36  students out of 60) of the students that did use recyclable bags who also thought recycling on campus was hard. With an approximately 1.1% difference in these percentage, the sample gives some reason to believe that the population of students at Flagler College believe that it is hard to recycle on campus.

 

Result 5: Phase 3: Contingency table   [Info]

Contingency table results:


Rows: Reusable Bag Usage
Columns: Difficult to Recycle on Campus
No, HardYes, EasyTotal
No553590
Yes362460
Total9159150

Chi-Square test:


StatisticDFValueP-value
Chi-square10.0186254420.8914

 

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 students used recycled bags  at Flagler College and the proportion of the population of students who do not use recycled bags

           Alternate: There is a difference in the proportion of the population of students use recycled bags at Flagler College and the proportion of the population of students who do not use recycled bags.

 

Prepare:

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

 

p-hat = (x1 + x2)/(n1 + n2) = (55 +36)/(90 +60) = 91/150 = 0.6067

           Sample One (no Self-Employed): Since n1*p-hat = 90(0.6067) = 54.6 ³ 10 and

                       n1*(1 – p-hat) = 90(1-0.6067) = 90(0.3933) = 35.40 ³ 10, sample one is large.

           Sample two (Self-Employed): Since n2*p-hat = 80(0.6733) = 53.9 ³ 10 and

                        n2*(1- p-hat) = 60(1-0.6067) = 60(0.3933) = 23.60 ³ 10, sample two is large.

2. Random Samples - Probably not but we hope they are representative. However, to proceed, we will assume that 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 students that want to be self-employed and those that do not.

 

Compute

Result 6: Phase 3: hypothesis test   [Info]

One sample proportion hypothesis test:


Outcomes in : Difficult to Recycle on Campus
Success : 91
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:
VariableCountTotalSample Prop.Std. Err.Z-StatP-value
Difficult to Recycle on Campus015000.040824829-12.2474491

 

Interpret

Since the p – value =0.4457 is more than the significance of 0.05, the null hypothesis will not be rejected. Therefore, there is sufficient evidence that there exists a difference in the proportion of the population of students who want to be self-employed and the proportion of the population of students who do not want to be self-employed who approve of Trump at Flagler College.

 

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 Trump as a president between the population of Flagler College students who want to be self-employed and those who do not. 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 Sampled with Independent Observations – Probably not but we hope it is representative. However, 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 (no Self-Employed): Since n1*p-hat1 = 70(0.285) = 19.9 ³ 10 and

                       n1*(1-p-hat1) = 70(1-0.285) = 70(0.715) = 50.1 ³ 10, sample one is large.

           Sample Two (Self-Employed): Since n2*p-hat2 = 80(0.363) = 29.0 ³ 10 and

                       n2*(1-p-hat2) = 80(1-0.363) = 80(0.637) = 50.9 ³10, sample two is large.

3. Big Population – Flagler College has a population of around 2500. Since we are unsure what overall percentage of the students do and do not support Trump, we will assume 50% are and 50% are not. Hence, there are approximately (0.50)(2500) = 1250 students who do support Trump and (0.50)(2500) = 1250 students that do not support Trump in the population.

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

Compute

 

Result 7: PHASE3:Two sample proportion summary confidence interval   [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 - p2559036600.0111111110.081489899-0.148606150.17082838

 

interpret

 

This confidence interval is for the most part positive. This indicates that the percentage of the population of all students use recyclable bags is less  than the percentage of the population of all students do use recyclable bags.. Thus, I am 95% confident that the percentage of all students that do not use recyclable bags is between 7% and 22.6% greater than the percentage of all students that do not want to be self-employed and approve of Trump.

 

Conclusion

This data show that majority of the students at Flagler College who do not use recyclable bags also believe that it is hard to recycle around campus. If recycling became more accessable to students on campus, or if students were infomated where recycling could be done then the results would have looked different.

 

 

 

Data set 1. MAT 223 Students and Recycling - Jesse, Shelby, an   [Info]
To analyze this data, please sign in.

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82735">Phase 3: Recycling </A>

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By jmcculloch173
Dec 6, 2018

PHASE THREE: Environmentally Friendly Habits of Students

Introduction:

On the first phase of this project, the environmentally friendly habits of students of a sample of 150 Flagler College students from fall semester 2018 were explored. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as those who use “Reusable Bags” and those who don’t use reusable bags labelled as “Non Reusable Bags”. There are 90 “No Reusable Bag” students and 60 “Reusable Bags”. A bat chart representing the two samples is presented below.

Result 1: Reusable Bag and Non Reusable Bag Students
<result1>

On this phase of the report, attention will be given to students’ opinions about the use of reusable bags.

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 do not use reusable bags while shopping. 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 reusable bags are not a priority when shopping.

Second, the sample results will also be used to determine if the opinion of the population of all Reusable Bag students and Non Reusable Bags students have a statistically significant difference of opinion regarding the effect of using Reusable bags when shopping. 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 Reusable Bag students and Non Reusable Bag students who use reusable bags when shopping.


Hypothesis Test #1- A Claim of Majority

In the sample of 150 students, 91 reported that it is difficult to recycle on campus. That is, the majority, 60,67%, of the students sampled expressed that recycling is difficult on campus. These sample results will be used to test the claim that the majority of the population of Flagler College students believe that recycling is difficult on campus at a level of significance of 0.05 A pie chart of the data is given below.

Result 2: Pie Chart With Data- Recycling on Campus- Is it Difficult
<result2>

Hypothesize
Null: Fifty percent of all Flagler College students believe that social media is a distraction to their day

Alternate: More than 50% of all Flagler College students believe that social media is a distraction to their day.

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 are both true statements, 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.

4. Independence within Sample – Yes, the student responses were taken in such a way that their responses were independent of each other.

Compute

Result 3: One sample proportion summary hypothesis test- Distraction
<result3>

Interpret

Since the p-value (<.0004 ) 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 it is difficult to recycle on campus.

Confidence Interval #1- Estimating the Population Proportion

The hypothesis test give sufficient evidence that the majority of all Flagler College students feel that recycling is difficult on campus. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that recycling on campus is difficult. Since a one tailed test with a level of significance of 0.05 was run, 90% confidence interval will be created.

Prepare


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