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Phase 3: Climate Change
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Introduction:

On the first phase of this project, we examined a sample of 150 Flagler College students from fall semester 2018 and their views on climate change. In the second phase, this same sample of 150 students was divided into two smaller 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 in a coastal area and the term “Non- Coastal Students” defined the sample of those Flagler College students who do not live in a coastal area. There are 98 Coastal Students and 52 Non- Coastal Students sampled. A pie chart representing the two samples is presented below.

Result 1: Where Students Live (Result 2)   [Info]
Right click to copy


On this phase of the report, attention will be given to students’ opinions on whether if they believe climate change.

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 believe in climate change. 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 think 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 their beliefs on 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 think climate change is real

Hypothesis Test #1- A Claim of Majority

In the sample of 150 students,  143 reported that they did think climate change was real. That is, the majority, 95.33%, 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 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: Students Views on Climate Change (Result 2)   [Info]
Right click to copy

Hypothesize

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

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

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




Prepare

  1. Random Sample- Probably not. We only sampled 150 Flagler students taking MAT 223, which is primarily taken by Freshman and Sophmore students; making the sample younger than the average college student (but we hope it is representative).

  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. Flagler College has a population of appropriately 2500

  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: Hypothesis test on Climate Change (Result 3)   [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
p1431500.953333330.04082482911.104354<0.0001

Interpret

Since the p-value (<0.0001) is less than the level of significance of 0.05, there is substantial evidence to reject the null hypothesis. Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students think that climate change is real.

Confidence Interval #1- Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students think 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 Observation- Probably not (but we hope it is representative). To proceed, we will assume it is. Also, the student responses were taken in such a way that their responses were independent of each other. Therefore, the sample is independent.

  2. Large Sample- Since n*phat= (150)(0.9533) = 143 > 10 and n*(1-phat)= (150)(1-0.9533)= (150)(0.0467)= 7< 10, the sample is not large(but we hope it is representative). However, to proceed, we will assume it is.

  3. Big Population- Since 10n= (10)(150)= 1500

Compute

Result 4: Confidence Interval on Climate Change   [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
p1431500.953333330.0172218640.925005890.98166078

Interpret

We are 90% confident that between 92.50% and 98.17% of all Flagler College students find that climate change is real. 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 their beliefs about climate change. Of the 98 Coastal Students, 92 think that climate change is real and of the 52 Non-Coastal Students, 51 think that climate change is real. That is. 93.9% (92 students out of 98) of the Coastal Students believe climate change is real and 98.1% (51 students out of 52) of the Non-Coastal Students believe climate change is real. With an approximately 4.2% difference in these percentages, the sample does not give statistical evidence 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 on whether climate change is real or not.  

 

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

Contingency table results:


Rows: Coastal Region
Columns: Climate Change
NoYesTotal
No15152
Yes69298
Total7143150

Chi-Square test:


StatisticDFValueP-value
Chi-square11.34665180.2459
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 think 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 think climate change is real.

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


Prepare:

1. Large Sample- It is found that the pooled sample proportion is p-hat= (x1+x2)/(n1+n2)= (92+51)/(98+52)= 143/150= 0.9533

Sample One (Coastal Students): Since n1* p-hat= (98)(0.9533)= 92> 10 and n1*(1- p-hat)= (98)(1- 0.9533)= (98)(0.0467)= 4.6

Sample Two (Non-Coastal Students): Since n2*p-hat= (52)(0.9533)= 51 >10 and n2*(1-p-hat)= (52)(1-0.9533)=(98)(0.0467)=1

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

Compute

 

Result 6: Hypothsis Test (Coastal V Non- Coastal)   [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 - p2515292980.0419937210.0361873431.16045330.2459

Interpret

Since the p-value= 0.2459 is more than the level of significance of 0.05, the null hypothesis will not be rejected. Therefore, there is not sufficient evidence that 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 think climate change is real.

Confidence Interval #2- Estimate the Difference between Two Population Proportions

The hypothesis test did not give 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 can 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. Also, yes, the student responses were taken in such a way that their response was independent of each other.

  2. Large Samples-

Sample One (Coastal Students): Since n1* p-hat1= (98)(0.939)= 92 > 10 and n18(1-p-hat1)= (98)(1-0.939)= (98)(0.061)= 6 < 10, sample one is not large (but we hope it is representative). However, to proceed, we will assume it is

Sample Two (Non-Coastal Students): Since n2*p-hat2= (52)(0.981)= 51 > 10 and n2*(1-p-hat2)= (52)(1-0.981)= (52)(0.019)= 1 > 10, sample two is not large (but we hope it is representative). However, to proceed, we will assume it is.

      3. Big Populations- Recall, Flagler College has a population of appropriately 2500 students. Since we are unsure what overall percentage of the students who do or do not believe in climate change, 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-Coastal Students in the population

Population One (Coastal Students): Since 10n1= (10)(98)= 980< 1250, population one is big.

Population Two (Non-Coastal Students): Since 10n2= (10)(52)= 520

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


Compute

 

Result 7: Confidence Interveal (Coastal V Non-Coastal)   [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 - p2515292980.0419937210.030809103-0.0183910120.10237845

Interpret

 

This confidence interval goes from negative to positive; this indicates that the percentage of the population of all Coastal Students who think climate change is real can statistically equal to the percentage of the population of all Non-Coastal Students who think climate change is real. Thus, I am 95% confident that the percentage of all Coastal Students who think climate change is real is not statistically different than the percentage of all Non-Coastal Students who think climate change is real.

Conclusion.

Climate Change has been a talking-point in American society ever since Al Gore’s documentary that discussed the scientific theory of climate change, titled An Inconvenient Truth, was released in 2006.   In this report, the sample provides evidence that the majority of all Flagler College students think climate change is real. In fact, it was estimated that between 92.50% and 98.16% of all Flagler College students believe that climate change is real. Furthermore, it was found that there is statistical evidence that the percent of the population of Flagler College students who believe in climate change is the same for students who live in a Coastal Students and Non-Coastal Students. It was found that Flagler College students have a widespread belief that climate change is real.

 

Climate Change has become an important topic in today’s society, that seems to be growing in importance every day. On Monday, November 26, the National Centers for Environmental Information publishing a report stating that “the global average temperature is much higher and is rising more rapidly than anything modern civilization has experience.” However, politicians are slow to make policy changes to help reduce carbon emission due to their privately held belief and the public’s belief in climate change. Hopefully, reports such as these that demonstrate that an overwhelming majority of a population believes in climate change will influence policymakers to adopt policies to help slow climate change. Or if not influence policymaking, at least mobilize voters and average Americans to support plans and initiatives that help slow the effects of climate change

 

Data set 1. Flagler College Students and Climate Change - Sydn   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82787">Phase 3: Climate Change </A>

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