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PHASE THREE: Climate Change Study
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INTRODUCTION

On the first phase of this project, we explored how familiar 2019 Flagler College spring semester students were with the effects of climate change.  In the second phase of the report, the same sample of 150 students were divided into two smaller samples. The two samples studied included the sample of Flagler College students who grew up in coastal regions (“coastal students”)  and the sample of Flagler College students who did not grow up in coastal regions (“non coastal students”). There were 89 coastal students and 61 non-coastal students sampled. A bar chart representing the two samples is presented below.


 

Result 1: Result 1: Bar Plot With Data   [Info]
Right click to copy


On this phase of the report, attention will be given to students’ belief about whether or not climate change exist.

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 real. 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 believe that climate change is real.

Second, the sample results will also be used to determine if the opinion of the population of all Coastal Students and the population of all Non coastal Students at Flagler College have a statistically significant difference of opinion regarding the existence of climate change. 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 coastal Students and non coastal Students who find that climate change is real.


Hypothesis Test #1 – A Claim of Majority


In the sample of 150 students, 142 reported that climate change is real.  That is, the majority, 94.67%, of the students sampled expressed that climate change is real. These sample results will be used to test the claim that the majority of the population of Flagler College students who believe that climate change is real at a level of significance of 0.05  A pie chart of the data is given below.


Result 2: Results 2 Pie Chart With Data Belief in Climate Change   [Info]
Right click to copy


Hypothesize

Null: Fifty percent of all Flagler College students believe that climate change is real.

Alternate: More than 50% of all Flagler College students believe that climate change is real.

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.


Result 3: Results 3 One sample proportion hypothesis test- Belief in Climate Change   [Info]

One sample proportion hypothesis test:


Outcomes in : Sample(Climate Change)
Success : Yes
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5

Hypothesis test results:
VariableCountTotalSample Prop.Std. Err.Z-StatP-value
Sample(Climate Change)1421500.946666670.04082482910.941054<0.0001


Interpret


Since the p-value (<0.0001) is less than the level of significance of 0.05, the null hypothesis must be rejected.  Therefore, there is sufficient evidence to fail to reject the the null hypothesis.


Confidence Interval #1 – Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that climate change is real. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that climate change is real. 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)(0.7133) = 107 > 10 and n*(1 – phat) = (150)(1 – 0.7133) = (150)(0.2867) = 43 > 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.


Result 4: Results 4 One sample proportion confidence interval   [Info]

One sample proportion confidence interval:


Outcomes in : Sample(Climate Change)
Success : Yes
p : Proportion of successes
Method: Standard-Wald

90% confidence interval results:
VariableCountTotalSample Prop.Std. Err.L. LimitU. Limit
Sample(Climate Change)1421500.946666670.018346460.916489430.97684391


We are 90% confident that between 91.6% and 97.7% of all Flagler College students believe in climate change.  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 coastal Students and the non coastal Students regarding the students beliefs in climate change. Of the 89 coastal Students, 85 believed in climate change. And of the 61 non coastal Students, 57 felt climate change is real.  That is, 95.5% (85 students out of 89) of the coastal Students did not believe in climate change, and 93.4% (57 out of the 61 students) of the non coastal Students did not believe in climate change. With an approximately 2% difference in these percentages, the sample gives little reason to believe that the population of coastal Students at Flagler College and the population of non coastal Students at Flagler College differ in their opinion that climate change is real.


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

Contingency table results:


Rows: Sample(Climate Change)
Columns: Sample(Coastal Region)
NoYesTotal
No448
Yes5785142
Total6189150

Chi-Square test:


StatisticDFValueP-value
Chi-square10.305090810.5807
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.


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 coastal Students at Flagler College and the proportion of the population of non coastal Students at Flagler College who believe that climate change is real.

Alternate: There is a difference in the proportion of the population of coastal Students at Flagler College and the proportion of the population of non coastal Students at Flagler College who believe that climate change is real.


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) = (85+57)/(89 + 61) = 142/150 = 0.9466

Sample One (coastal Students): Since n1*p-hat = (89)(0.9466) = 84.25 > 10 and

n1*(1 - p-hat) = (89)(1 – 0.9466) = (81)(0.0534) = 4.33 <10, sample 1 is not large enough to have an accurate representation of the population.

Sample Two (non coastal Students): Since n2*p-hat = (61)(0.9466) = 57.7 > 10 and

n2*(1 - p-hat) = (61)(1 – 0.9466) = (61)(0.0534)) = 3.25< 10, sample 2 is not large enough to have an accurate representation of the population.

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 coastal Students and the non coastal Students.



Result 6: Results 6 Two sample proportion hypothesis test   [Info]

Two sample proportion hypothesis test:


p1 : Proportion of successes (Success = Yes) for Sample(Coastal Region)
p2 : Proportion of successes (Success = Yes) for Sample(Climate Change)
p1 - p2 : Difference in proportions
H0 : p1 - p2 = 0
HA : p1 - p2 ≠ 0

Hypothesis test results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.Z-StatP-value
p1 - p289150142150-0.353333330.048593552-7.2711978<0.0001


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 coastal Students at Flagler College and the proportion of the population of non coastal Students at Flagler College who think climate change is real.


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 change is real between the population of coastal Students at Flagler College and the population of non coastal Students at Flagler College. 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 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.

2. Large Samples

Sample One (coastal Students): Since n1*p-hat1 = (89)(0.9466) = 84.25  > 10 and

n1*(1 - p-hat) = (89)(1 – 0.9466) = (89)(0.0534) = 4.33 10, sample one is large.


Sample Two (non coastal Students): Since n2*p-hat2 = (61)(0.9466) = 57.7 > 10 and

n2*(1 - p-hat2) = (61)(1 – 0.9466 = (61)(0.0534) = 3.3 < 10, sample 2 is not large enough to have an accurate representation of the population.

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 coastal Students and (0.50)(2500) = 1250 students who are non costal Students in the population.

Population One (coastal Students): Since 10n1 = (10)(89) = 890< 1250, population one not large enough to have an accurate representation of the population.

Population Two (non coastal Students): Since 10n2 = (10)(61) = 610 < 1250, population 2 not large enough to have an accurate representation of the population.  

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


Result 7: Results 7 Two sample proportion confidence interval   [Info]

Two sample proportion confidence interval:


p1 : Proportion of successes (Success = Yes) for Sample(Coastal Region)
p2 : Proportion of successes (Success = Yes) for Sample(Climate Change)
p1 - p2 : Difference in proportions

95% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p289150142150-0.353333330.044104254-0.43977608-0.26689058


Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all coastal Students who feel climate change is real is less than the percentage of the population of all non-coastal Students who feel climate change is real.  Thus, I am 95% confident that the percentage of all non coastal Students who feel climate change exist is between 26.7% and 44.0% greater than the percentage of all coastal Students who feel climate change is real.


Conclusion

People have began to recognize the devastating effects of human impact modeled by climate change. In this report, it was revealed that over 90% of the given sample of students believed in climate change. In fact, it was estimated that between 91.6% and 97.7% of all Flagler College students believe that climate change is real. Little evidence was found to support the belief that more students who grew up near and coast (and were more prone to the effects of climate change) would believe as opposed to students who did not grow up near a coast.  It was estimated that between 26.7% and 44.0% more of all Flagler College students who did not grow up near the coast believed in climate change than all other Flagler College students. Clearly the belief of climate change is not limited to one specific geographical location. Technology has certainly contributed to such a high number of believers. It is not that shocking how well known the social issue has become in past years. Perhaps a newly released documentary that illustrates the effects of global warming would even increase the number of believers. Although enforcing such a policy that would be difficult, it is something to consider. Times is ticking and it won't be long before the effects of climate destroy our Earth. As the world wouldn't exist without skeptics, neither would statistics.   


Data set 1. Sassi-Pearce-Maloney-Sampled from Flagler College   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=87130">PHASE THREE: Climate Change Study</A>

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