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Phase Three - Flagler College Students and Climate Change - ChunYan Leong
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Introduction

During the first phase of our statistics project, the understanding and effects of climate change were explored amongst 150 Flagler College students from the fall semester.  During the second phase of the project, this same sample of 150 students were divided into two samples which were referred to as the Coastal Students and the Non Coastal Students.  The term “Coastal Students” defined the sample of those Flagler College students who live near a coastal area and the term “Non-Coastal Students” defined the sample of those Flagler College students who do not live near a coastal area.  There are 102 Coastal Students and 48 Non-Coastal Students in the sample. A bar chart representing the two samples is presented below.


Result 1: Coastal and Non-Coastal Students bar graph   [Info]
Right click to copy



During this phase of the report, attention will be given to students’ opinions about living in a coastal area compared to living in a non-coastal area.

 

To start off with, methods of statistical inference will be used to determine if the sample results indicate that the majority of all Flagler College students feel that there is a higher chance of experiencing higher dramatic climatic events when living in a coastal region. We will start off with a hypothesis test to find statistical evidence and then a confidence interval will be created to estimate the percentage of the population of Flagler College students who feel coastal areas have a higher chance of being affected by dramatic climatic events.

 

 

After that, 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 statistical difference in opinion regarding the dramatic climatic events caused by the areas they live in. Once again, a hypothesis test will be done to find statistical evidence 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.


Hypothesis Test #1 - A Claim Of Majority

 

 In the sample of 150 students, 102 reported that they were affected by a dramatic climatic event.  That is, the majority, which is 68% of the students sampled, expressed that living in a coastal area means there is a higher chance of being affected by some sort of climatic event.  These sample results will be used to test the claim that the majority of the population of Flagler College students believe that living in a coastal area means there in a higher chance of getting affected by a climatic event at a level of significance of 0.05  A pie chart of the data is given below.


 

Result 2: Pie Chart With Summary Effected by Climatic Eevents   [Info]
Right click to copy

 


Hypothesize

 

Null Hypothesis:Fifty percent of all Flagler College students believe that living in coastal areas result in a higher chance of experiencing a climatic event.            

 

Alternate Hypothesis: More than 50% of all Flagler College students believe that climatic events are more common near coastal areas. So based on the alternate hypothesis, this is a right-sided test.

 

Prepare

 

1. Random Sample – Not a random sample. Although in order 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 around 2500 students.

              

 

4. Independence within Sample – Yes, the student responses were taken in a specific way that their responses were independent.


Compute

 

 

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
p1021500.680.0408248294.4090815<0.0001

 

 

Interpret

 

Since the p-value is less than the level of significance of 0.05, the null hypothesis has to be rejected. Therefore, there is sufficient evidence to support the claim that a majority of Flagler College students feel that living in a coastal area means there is a higher chance of getting his by a climatic event


Confidence Interval #1 – Estimating the Population Proportion


The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that living in a coastal area increases their chances of experiencing a climatic event at some point of time. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe living in a coastal area increases their chances of experiencing a climatic event. 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 – Once again, this is probably not a random sample, however we will proceed and assume that 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)(0.68) = 102 > 10 and n*(1 – phat) = (150)(1 – 0.68) = (150)(0.32) = 48 > 10, the sample is large.

              

 

3. Big Population – Since 10n = (10)(150) = 1500 < 2500, the population is big.  Recall, Flagler College has a population around 2500 students.


Compute


 

Result 4: One sample proportion summary confidence interval Coastal and Non Coastal   [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
p1021500.680.0380876180.617351440.74264856

 


Interpret

 

We are 90% confident that between 61.7% and 74.3% of all Flagler College students find that living in a coastal area increases your chances of experiencing a climatic event. 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 Not Coastal Students regarding if they believed climate change was real.  Of the 102 Coastal Students, 99 felt that climate change is real and of the 48 Not Coastal Students, 47 felt that climate change is real. That is, 97.06% (99 students out of 102) of the Coastal Students felt that climate change is real and 97.92% (47 students out of the 48 students) of the Not Coastal Students felt that climate change is real.  With an approximately 0.86% difference in these percentage, the sample gives very little reason to believe that the population of Coastal Students at Flagler College and the population of Not Coastal Students at Flagler College differ in their opinion that climate change is real.

 


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

Contingency table results:


Rows: (Coastal Region)
Columns: (Number of Dramatic Climatic Events in Life Time)
01234567891012131415182025Total
No77469331200001103148
Yes76691818965162103113102
Total1413101527211277162114144150

Chi-Square test:


StatisticDFValueP-value
Chi-square1720.9195220.2299
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 Not Coastal Students at Flagler College who feel 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 Not Coastal Students at Flagler College who feel 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) = (47 + 99)/(48 + 102) = 146/150 = 0.9733

 

Sample One (Coastal Students): Since n1*p-hat = (48)(0.9733) = 46.72 > 10 and

 

n1*(1 - p-hat) = (48)(1 – 0.9733) = (48)(0.02667) = 1.28016 > 10, sample one is large.

 

Sample Two (Not Coastal Students): Since n2*p-hat = (102)(0.9733) = 99.2766 > 10 and

 

n2*(1 - p-hat) = (102)(1 –0.9733) = (102)(0.02667) = 2.7234 > 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 Coastal Students and the Not Coastal Students.

 


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 - p2102150481500.360.0577350276.2353829<0.0001



Interpret

Since the p – value = 0.761 is more 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 Not Coastal Students at Flagler College who feel 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 Not 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-hat = (48)(0.9733) = 46.72 > 10 and

 

n1*(1 - p-hat) = (48)(1 – 0.9733) = (48)(0.02667) = 1.28016 > 10, sample one is large.

 

Sample Two (Not Coastal Students):Since n2*p-hat = (102)(0.9733) = 99.2766 > 10 and

 

n2*(1 - p-hat) = (102)(1 –0.9733) = (102)(0.02667) = 2.7234 > 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 believe that climate change is real, we will assume 50% do and 50% do not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Coastal Students and (0.50)(2500) = 1250 students who are Not Coastal Students in the population.

 

Population One (Coastal Students): Since 10n1 = (10)(48) = 480 < 1250, population one is big.

 

Population Two (Not Coastal Students): Since 10n2 = (10)(102) = 1020 < 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.

 

 

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

90% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p2102150481500.360.0538640260.271401560.44859844

 

 

Interpret

 

This confidence interval is both negative and positive; 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 Not Coastal Students who feel climate change is real.  Thus, I am 95% confident that the percentage of all Not Coastal Students who feel climate change is between 4.3% and 6.1% greater than the percentage of all Coastal Students who feel climate change is real.

 

Conclusion

 

 

Society has embraced that climate change is something of a pressing issue.  In this report, the sample provided evidence that the majority of all Flagler College students believe that climate change is real.  In fact, it was estimated that between 61.7% and 74.3% of all Flagler College students believe that climate change is real. Furthermore, it was found that there is statistical evidence to prove that those students who do live and do not live in a coastal region believe that climate change is real.  It was estimated that between 4.3% and 6.1% more of all Flagler College students who live in a coastal environment believed a little more than most flagler students believe that climate change is real. This is natural association to me. I feel that our climate is changing at a more rapid rate than usual. I feel that being more environmentally friendly will help save earth little by little. I know that I am not alone in this. It is our goal to keep this planet healthy and safe to live on instead of just taking it for granted. We have been gifted with the opportunity to live here, so we should do our part by taking care of the place we call home.


 




 

 

 

 

 


 

 

 

 

 

 

Data set 1. Flagler College Students and Climate Change - Leon   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82845">Phase Three - Flagler College Students and Climate Change - ChunYan Leong</A>

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