PHASE 3  Fjolnisson, Kelley, and Taylor  Flagler College Students and Recycling Spring 2019
Introduction:
On the first phase of this project, the question, ‘‘If Flagler College makes it easy or hard for the community to recycle’’ and a sample of 150 Flagler College students answered, from a survey conducted in Spring 2019 which was explored. In the Second phase, this sample of 150 students was divided into two smaller samples which were referred to as the ones who said ‘’Yes, easy’’ along with those who said ‘’No, hard’’. Those who said it was ‘’easy’’ defined the sample of those Flagler College students who do not feel that Flagler College makes it easy for the community or students to recycle. Those who said it was ‘’hard’’ defined the sample of those Flagler College students who do not feel that Flagler College makes it hard for the community or students to recycle. There are 88 who said it was ‘’hard’’ and 62 who said it was ‘’easy’’ of the students sampled. A bar chart is representing the two samples is presented below.
On the first phase of the project, attention will be given to students’ opinions about if plastic straws should be banned, which are spreading all over the world because of the negative impact on the community.
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 plastic straws should be banned. A hypothesis test will first be run to find statistical evidence of majority and then confidence interval will be created to estimate the percentage of the population of Flagler College students who feel that plastic straws should be banned.
Second, the sample results will also be used to determine if the population of all students who found it ‘’easy’’ to recycle in the Flagler Community and the population of all students who found it ‘’hard’’ to recycle in the Flagler Community have a statistically significant difference of opinion regarding the ban of plastic straws. 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 Students who found it ‘’hard’’ and ‘’easy’’ to recycle in the Flagler College community who find that we should ban plastic straws.
Hypothesis test #1  A Claim of Majority
In the sample of 150 students, 94 reported that we should ban, plastic drinking straws. That is the majority, 62.67%, of the student's samples, expressed that we should ban plastic drinking straws. These sample results will be used to claim that the majority of the population of Flagler College students view that we should ban plastic straws at a level of significance 0.05. A pie chart is given below.
Hypothesize:
Null: Approximately 62.67% of all Flagler College students believe that we should ban plastic drinking straws.
Alternate: More than 50% of students of all Flagler College students believe that we should ban plastic drinking straws.
Based on the alternate hypothesis, this is a rightsided test.
Prepare:
1. Random Sample with Independent Observations – Yes, the way the sample was selected was random and the way that the survey was conducted makes the observation independent.
2. Large Sample – Since np0 = (150)(0.50) = 75 > 10 and n*(1 – p0) = (150)(1 – 0.50) 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 (0.001) 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 we should ban plastic drinking straws.
Confidence Interval #1  Estimating the population proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that we should ban plastic drinking straws. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler college students who believe that plastic drinking straws should be banned. Since the onetailed 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 – Yes, the way the sample was selected was random and the way that the survey was conducted makes the observation independent.
2. Large Sample – Since np0 = (150)(0.6267) = 94 > 10 and n*(1 – p0) = (150)(1 – 0.6267) = 56 > 10 both statements are true, the sample is large.
3. Big Population – Since 10n = (10)(150) = 1500 < 2500, the population is big. Flagler College has a population of approximately 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 56.2 % and 69.2% of all Flagler College students find that we should ban plastic straw drinking. This is certainly the majority of all Flagler College Students.
Hypothesis Test #2  A Claim of the Difference between Population Proportions
A contingency table was created to compare the opinions of student’s that found it ‘’hard’’ to recycle in the Flagler community and student’s that found it ‘’easy’’ regarding to the ban of plastic drinking straws. Of the 88 who found it ‘’hard’’ to recycle in the Flagler community, 58 were in favour of the banning of plastic straws, approximately 66%. Of the 62 who found it ‘’easy’’ to recycle in the Flagler community, 36 were in favour of the banning og plastic straws, approximately 58%. With an approximately 8% difference in these percentage, the sample gives some reason to believe that the population of students of Flagler College who found it ‘’hard’’ to recycle in the Flagler Community and the population of students of Flagler College who found it ‘’easy’’ to recycle in the Flagler Community differ slightly in their opinion of the banning of plastic drinking straws.
Contingency table results:Rows: Do you think Flagler College makes it easy or hard for the college community to recycle? Columns: Do you think plastic drinking straws should be banned?
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 at 0.05.
Hypothesize:
Null: There is no difference in the proportion of the population of Flagler College student’s who found it ’’easy’’ or ’’hard’’ who feel that we should ban plastic drinking straws.
Alternate: There is a difference in the proportion of the population of Flagler College student’s who found it ’’easy’’ or ’’hard’’ who feel that we should ban plastic drinking straws.
Based on the alternate hypothesis, this is a twotailed test.
Prepare:
1. Large Samples – It is found that the pooled sample proportion is
phat = (x1 + x2)/(n1 + n2) = (58+36)/(88 + 62) = 94/150 = 0.626
Sample One (Hard to recycle): Since n1*phat = (88)(0.626) = 55.1 > 10 and n1*(1  phat) = (81)(1 – 00.626) = (81)(0.374) = 30.3 > 10, sample one is large.
Sample Two (Easy to recycle): Since n2*phat = (62)(0.626) = 38.8 > 10 and
n2*(1  phat) = (62)(1 –0.626) = (62)(0.374) = 23.2 > 10, sample two is large.
2. Random Samples – 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 married parents and unmarried parents.
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 pvalue = 0.328 is more than the level of significance of 0.05, the null hypothesis will not be rejected, there is insufficient evidence that there exists a difference in the proportion of the population of students who found it ‘’hard’’ to recycle in the Flagler College community and the proportion of the population of students who found it ‘’easy’’ to recycle in the Flagler College community who feel that we should ban the plastic drinking straws.
Confidence Interval #2  Estimate the difference between Two Population Proportions
The hypothesis test gave us insufficient evidence that there is a significant difference in the opinion that students feel that we should ban plastic drinking straws between the population of Flagler College students who found it ‘’hard’’ to recycle in the Flagler community and Flagler College students who found it ‘’easy’’ to recycle in the Flagler community, therefore a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions cannot be equal. Since a twotailed 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. However, to proceed, we will assume it is. Furthermore, yes the student's responses were taken in such a way that their responses were independent of each other.
2. Large Samples –
Sample One (hard to recycle): Since n1*phat = (88)(0.66) = 58.08 > 10 and n1*(1 
phat) = (88)(1 – 0.66) = (88)(0.34) = 29.92 > 10, sample one is large.
Sample Two (easy to recycle): Since n2*phat = (62)(0.66) = 40.92 > 10 and n2*(1  phat) = (62)(1 –0.66) = (62)(0.34) = 21.1 > 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 are or are not affected socially by social media, we will assume 50% is and 50% are not. Hence, there are not approximately (0.50)(2500)= 1250 students who found it is ’’easy’’ to recycle in the Flagler community and (0.50)(2500) = 1250 students who found it ’’hard’’ to recycle in the Flagler community in the population.
Population One (hard to recycle): Since 10n1 = (10)(88) = 880 < 1250, population one is big
Population Two (easy to recycle): Since 10n2 = (10)(62) = 620 < 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
Since the pvalue = 0.328 which is more than the level of significance of 0.05, the null hypothesis will not be rejected. Therefore, there is insufficient evidence that there exists a difference in the proportion of the population of students of Flagler College who found it ‘’easy’’ to recycle in the Flagler College community and the proportion of the population of students of Flagler College who found it ‘’hard’’ to recycle in the Flagler College community who feel that we should ban the police.
Conclusion:
It seems that people are growing more and more concerned about the importance of recycling. In this report, the sample provided evidence that the majority of all Flagler College Students find that we should ban plastic drinking straws. In fact, it was estimated that between 56.2% and 69.2% of all Flagler College students find that we should ban plastic drinking straws. Furthermore, it was found that there is statistical evidence that those students who find it ‘’hard’’ to recycle in Flagler Community are more in favour of banning plastic drinking straws, which seems that they are more concerned with recycling in general. It was estimated that between 0% and 24% more of all Flagler College students with feelings that it is ‘’hard’’ to recycle in the Flagler community were in favour of banning plastic drinking straws more than all other Flagler College students. This is a natural association for me. I feel those who are more concerned about recycling should be in favour of banning plastic straw drinking which has devastatingly dangerous effects on the environment.
The underlying purpose of recycling is to help protect the environment. According to the website, recyclingguide.org.uk about why recycling is important it lists, ‘’Recycling is very important as waste has a huge negative impact on the natural environment. Harmful chemicals and greenhouse gasses are released from rubbish in landfill sites’’ (recycling guide). As from personal experience, I was educated at a Restaurant that I worked for on the reason why the restaurant banned plastic drinking straws, that the main reason for eliminating plastic straws is because of their negative impact on our oceans and marine wildlife. We should definitely try to improve our current recycling situation at Flagler College, talking from my own personal experience there aren’t too many recycling trash cans on the campus as I would like to. The world must also be encouraged to recycle to help protect our environment, that is ever so important to us! Without it, our chances of survival are slim. Bring more education about the dangers of not recycling plastics to all schools and advertise it more on the internet which is where most people get their information from.
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:

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