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Phase Three: Flagler Students and Climate Change Spring 2019
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Introduction:

On the first phase of this project, the opinions on and experience with climate change of a sample of 150 Flagler College students from Spring semester 2019 was explored.  In this phase of the report, this same sample of 150 students will be divided into two smaller samples. The two samples are the sample of Flagler College students who believed that climatic change is human made and those who believe it is natural made cycle. For the sake of clarity, these groups may be referred to as the “Human Made” and “Natural” groups. There are 127 students who believe climatic is human made and 23 students believe it was naturally made. A bar chart representative of this group is shown below.

Result 1: Students who believe Climate Change is Human Induced   [Info]


 


On this phase of the report, attention will be given to students’ opinions about climate change being natural or human induced.

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 climate change is anthropogenic.  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 climate change stems from human causes.

Second, the sample results will also be used to determine if the opinion of the population of all of the students who believe climate change is human induced and the population of all of the students who believe climate change is natural at Flagler College have a statistically significant difference of opinion regarding their agreeance or disagreeance with the Paris Climate Accord.

Lastly, we will observe the opinions on whether or not the students in the human made or natural groups believe that there has been an increase in Dramatic Climate. Thus, we will determine if opinions on dramatic climate change differ significantly between those of the Human Made and Natural groups of students.

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 Human Made students and Natural Students who agree or disagree with the Paris Climate Accord, as well as each for Human Made and Natural Students regarding their opinions on whether theres has been an increase on Dramatic Climate.


Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 120 students reported that they disagree with the Paris Climate Accord.  That is, the majority, 80%, of the students sampled expressed they do not agree with the Paris Climate Accord. The remaining 30 students, making up 20% of the population, do agree with the Paris Climate Accord.These sample results will be used to test the claim that the majority of the population of Flagler College students do NOT agree with the Paris Climate Accord 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 disagree with the Paris Climate Accord.

             Alternate: More than 50% of all Flagler College students disagree with the Paris Climate       Accord.

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

Prepare

             1. Random Sample – Not completely, as all students surveyed happen to be in Statistics class during Spring 2019. However, we will proceed with this comparison.

             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   [Info]


 


nterpret

Since the p-value (

 

Confidence Interval #1 – Estimating the Population Proportion

             The hypothesis test gives sufficient evidence that the majority of all Flagler College students disagree with the Paris Climate Accord being put into action.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who agreed that Paris Climate Accord shouldn't be put into action.  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)(0.8000) = 120 > 10 and n*(1 – phat) = (150)(1 – 0.8000) = (150)(0.2000) = 30 > 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


 


Interpret

We are 90% confident that between 74.6% and 85.4% of all Flagler College students who agreed that Paris Climate Accord shouldn't be put into action.  As both the upper and lower limit are above 50%, 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 Human Made and the Natural Cycle Students regarding increases of dramatic climatic events and whether or not climate change is human made or natural cycle.  Of the 15 Decrease Students,11 felt that climate change was natural cycle and of the 135 Increase Students, 12 felt that climate change is natural cycle.  That is, 73.3% (11 students out of 15) of the Decrease Students felt that climate change is natural cycleand 8.8% (12 students out of the 135 students) of the Increase Students felt that climate change was natural cycle.  With an approximately 64.5% difference in these percentage, the sample gives some reason to believe that the population of Increase Students at Flagler College and the population of Decrease Students at Flagler College differ in their opinion that climate change was natural cycle.

 

 

 


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 Increase Students at Flagler College and the proportion of the population of Unsocial Students at Flagler College who feel climate change is natural cycle.

Alternate: There is a difference in the proportion of the population of Social Students at Flagler College and the proportion of the population of Increase Students at Flagler College who feel climate change is natural cycle.

Based on the alternate hypothesis, this is a two tailed test.

Prepare:

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

 

p-hat = (x1 + x2)/(n1 + n2) = (11 + 12)/(15 + 135) = 23/150 = 0.1533

Sample One(Decrease Students):Since n1*p-hat = (15)(0.1533) = 2.3 < 10 and

n1*(1 - p-hat) = (15)(1 – 0.1533) = (15)(0.8467) =12.7 > 10, sample one is small.

Sample Two (Increase Students):Since n2*p-hat = (135)(0.1533) = 21 > 10 and

n2*(1 - p-hat) = (135)(1 – 0.1533) = (135)(0.8467) = 114.3 > 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 Increase Students and the Decrease Students.

 

Compute

 

 

 


Interpret

Since the p – value = 0.0001 is less than the level of significance of 0.05, the null hypothesis will be rejected.  Therefore, there is sufficient evidence that there exists a difference in the proportion of the population of Increase Students at Flagler College and the proportion of the population of Decrease Students at Flagler College who feel climate change is natural cycle.

 

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 that climate is dramatically increasing between the population of Human Made Students at Flagler College and the population of Natural Students at Flagler College. Therefore, a confidence interval will be created to estimate this difference and potentially 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.

p-hat = (x1 + x2)/(n1 + n2) = (11 + 12)/(15 + 135) = 23/150 = 0.1533

Sample One(Decrease Students):Since n1*p-hat = (15)(0.1533) = 2.3 < 10 and

n1*(1 - p-hat) = (15)(1 – 0.1533) = (15)(0.8467) =12.7 > 10, sample one is small.

Sample Two (Increase Students):Since n2*p-hat = (135)(0.1533) = 21 > 10 and

n2*(1 - p-hat) = (135)(1 – 0.1533) = (135)(0.8467) = 114.3 > 10, sample two is large.

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 Increase Students and the Decrease Students.

 

 

5. Big Populations – Recall, Flagler College has a population of appropriately 2500 students.  Since our group consists of humans who have undoubtedly experienced the environment, we will use the entire population of 2500 students. In other words, there is no reason to split the population as there is no chance of a group of students not being able to develop an experienced opinion on Climate.

Population One (Decrease Students): Since 10n1 = (10)(15) = 150 < 2500, population one is big.

Population Two (Increase Students): Since 10n2 = (10)(135) = 1350 < 2500, 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


 

 


Interpret


This confidence interval is almost completely negative; this indicates that the percentage of the population of all Natural Students that believe Climate is dramatically increasing is less that Human Made students that believe Climate is increasing.  Thus, I am 90% confident that the percentage of all Natural Students who believe the Climate is Dramatically increasing is between 11.6% less than the percentage of all Human Made students that believe the Climate is Dramatically increasing. There is a minor, highly unlikely, window of .9% possibility that the proportion is reversed.


Conclusion

Society has embraced climate change and the consequences that climate change can have on our daily life is an important topic.  In this report, the sample provided evidence that the majority of all Flagler College students disagree with the Paris Climate Accord. It was also discovered that of the students who find climate change is increasing, also believe it is human made. These tests correlate directly in that the largest numbers belong to the Human Made group.  In fact, it was estimated that between 41.5% and 87.3% of all Flagler College students find that climate change increasing and human made. Furthermore, it was found that there is statistical evidence that those students who feel climate change is increasing tend to belong to the Human Made group of students.73.3% (11 students out of 15) of the Decrease Students felt that climate change is natural cycle and 8.8% (12 students out of the 135 students) of the Increase Students felt that climate change was natural cycle.  This is natural association to me. I would assume that if someone disagreed with Climate Increasing, they would probably agree that any Climate Change is just due to earth’s natural cycle..

 

As a take away, it might be beneficial to reflect on underlying factors to certain opinions. As we observed, those who disagreed with the Paris Climate Accord and those who did not believe climate was dramatically increasing majorly belonged to the group of Natural students. Therefore, it is assumable that their opinions on these two subjects likely stem from their underlying belief that climate change is NOT human induced. From this study, we can learn to either be objective in our persuasion or work from the ground up. That is, if trying to reach someone on a certain topic, aim for the roots of their understanding, rather than the immediate issue to be discussed.


Result 1: Bar Plot With Data   [Info]
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Result 2: Pie Chart With Data   [Info]
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Result 3: One sample proportion summary hypothesis 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
p1201500.80.0408248297.3484692<0.0001

Result 4: One sample proportion summary 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
p1201500.80.0326598630.746279310.85372069

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

Contingency table results:


Rows: Sample(Increase in Dramatic Climactic)
Columns: Human Made or Natural Cycle
Human MadeNatural CycleTotal
No41115
Yes12312135
Total12723150

Chi-Square test:


StatisticDFValueP-value
Chi-square143.187265<0.0001
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Result 6: Two sample proportion summary hypothesis test   [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 - p21115121350.644444440.0980635556.5717018<0.0001

Result 7: 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 - p21115121350.644444440.116777330.415565080.87332381

Data set 1. Flagler College Students and Climate Change Spring   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=86952">Phase Three: Flagler Students and Climate Change Spring 2019</A>

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