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Created: Dec 6, 2018
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Phase 3 - Climate Change (Sargent, Wyman, Robertson)
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Introduction:

On the first phase of this project, the climate change opinions of a sample of 150 Flagler College students from fall semester 2018 was explored.  In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as the Coastal Region Students and the Non Coastal Region Students.  The term “coastal Students” defined the sample of those Flagler College students who lived in a coastal region and the term “Non coastal Students” defined the sample of those Flagler College students who do not live on the coast.  There are 100 coastal Students and 50 Non coastal Students sampled. A bar chart representing the two samples is presented below.


Result 1: Coastal Students and Non Coastal Students Sampled

 

On this phase of the report, attention will be given to students’ opinions about climate change based on if they work in a coastal or non coastal region.

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 human.  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 feel that climate change is man made or naturally occuring.

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 weather climate change is naturally occurring or manmade.  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 believe climate change is naturally occurring or manmade.


Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 126 students reported that climate change was man made.  That is, the majority, 84%, of the students sampled expressed that climate change is manmade.  These sample results will be used to test the claim that the majority of the population of Flagler College students view climate change as human made at a level of significance 0.05  A pie chart of the data is given below.

 

Result 2: Pie Chart with Data – Climate Change – Is climate change man-made or natural cycle?

 


Hypothesize

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

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

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.

Compute



Result 3: One sample proportion summary hypothesis test - Non Coastal


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 support the claim that the majority of all Flagler College students feel that climate change is manmade.

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 man made.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe climate change is man made.  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)(0.84) = 126 > 10 and n*(1 – phat) = (150)(1 – 0.84) = (150)(0.16) = 24 > 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 One sample proportion summary confidence interval - Non Coastal

 

Interpret

We are 90% confident that between79.08% and 88.92% of all Flagler College students find that climate change is man made.  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 cause of climate change.  Of the 100 coastal Students,84 felt climate change was man made and of the 50of the Non coastal Students, 42 felt climate change was man made.  That is,84% (84 students out of 100) of the coastal Students felt climate change was man made and 84% (42 students out of the 50 students) of the Non coastal Students felt climate change was man made.  With an approximately 0% difference in these percentage, the sample gives some reason to believe that the population of coastal Students at Flagler College and the population of Non coastal Students at Flagler College are the same in their opinion that climate change is manmade.


Result 5: Contingency table (with data) - Man Made vs. 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 coastal Students at Flagler College and the proportion of the population of Non coastal Students at Flagler College who feel climate change is man made.

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 feel climate change is man made.

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) = (84 + 16)/(126 + 24) = 100/150 = 0.667

Sample One (coastal Students): Since n1*p-hat = (126)(0.84) = 105.84 > 10 and

n1*(1 - p-hat) = (126)(1 – 0.84) = (126)(0.16) = 20.16 > 10, sample one is large.

Sample Two (Non coastal Students): Since n2*p-hat =(24)(0.84) = 20.16 > 10 and

n2*(1 - p-hat) = (24)(1 – 0.84) = (126)(0.16) = 20.16 > 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 Non coastal Students.

 


Result 6: Two sample proportion summary hypothesis test - Non Coastal student Vs. Man Made

 

Since the p – value = 0.0001 is lessthan 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 feel climate change is manmade.

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 man made 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 = (50)(0.84) = 42 > 10 and

n1*(1 - p-hat1) = (100)(1 – 0.84) = (50)(0.16) = 8 < 10, sample one is small.

Sample Two (Non Coastal Students): Since n2*p-hat2 = (100)(.84) = 84 > 10 and

n2*(1 - p-hat2) = (100)(1 – 0.84) = (100)(0.16) = 16 > 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 who believe climate change is manmade, 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)(50) = 500 < 1250, population one is big.

Population Two (Non coastal Students): Since 10n2 = (10)(100) = 1000 < 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 - coastal Vs. Non coastal  

 

This confidence interval is both positive and negative: this indicates that the percentage of the population of all coastal Students who feel climate change is manmade is equal to the percentage of the population of all Non coastal Students who feel climate change is manmade.  Thus, I am 95% confident that the percentage of all non-coastal students who feel climate change is man-made is between -12.46% and 12.46% and equal the percentage of all coastal Students who feel climate change is manmade.


Conclusion

Society has embraced climate change and the consequences that climate change makes on our daily life is an important topic.  In this report, the sample provided evidence that the majority of all Flagler College students find climate change is manmade.  In fact, it was estimated that between79.08% and 88.92%of all Flagler College students find that climate change is man made.  Furthermore, it was found that there is statistical evidence that those students who are from a coastal region are more likely to believe that climate change is manmade.  It was estimated that between -12.46% and 12.46% more of all Flagler College students from coastal regions felt that climate change was manmade than all other Flagler College students.  This is natural association to me. I feel that climate change is definitely man made because it is happening at such a rapid pace.

The underlying purpose mankind is to help the earth not hurt it.  Hence, it is interesting that the majority of students believe that climate change is manmade.  Maybe a class about how to save the earth, or more eco friendly reports in the media could possibly strike up a conversation amongst students to figure out what they can do for a change.  It may give the students an edge of being more eco friendly and get more inspired to help the earth they live in. Although creating an eco friendly class could be difficult, it is something to consider.  On the other hand getting students thinking and talking about climate change should not only take place in a classroom, students should be able to see how cool the earth is and want to do something to help.  Times are always changing, but humans are creature of habit so hopefully a we can break the chain and help to save the earth one stats project at a time.

 

Result 1: Result 1 Bar Graph Costal Region   [Info]
Right click to copy

Result 2: Result 2 Pie Chart Human Made or Natural Cycle   [Info]
Right click to copy

Result 3: One sample proportion summary hypothesis test (RESULT 3 PHASE 2)   [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
p1261500.840.0408248298.3282651<0.0001

Result 4: One sample proportion summary confidence interval (RESULT 4 PHASE 2)   [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
p1261500.840.0299332590.790764170.88923583

Result 5: Contingency table Human Made or Natural Cycle   [Info]

Contingency table results:


Rows: Human Made or Natural Cycle
Columns: Coastal Region

Cell format
Count
(Expected count)

NoYesTotal
Human Made42
(42)
84
(84)
126
Natural Cycle8
(8)
16
(16)
24
Total50100150

Chi-Square test:


StatisticDFValueP-value
Chi-square12.0309412e-281

Result 6: Two sample proportion summary hypothesis test (PHASE TWO)   [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 - p242508410000.06349803101

Result 7: Two sample proportion summary confidence interval (PHASE 2 RESULT7)   [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 - p242508410000.063498031-0.124453850.12445385

Data set 1. Flagler College Students and Climate Change   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82716">Phase 3 - Climate Change (Sargent, Wyman, Robertson)</A>

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