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Phase Three: Flagler College Students views on Global Warming and Climate Change
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Introduction:

 

On the first phase of this project, the views on global warming and climate change of a sample of 150 Flagler College students from fall semester 2017 and spring semester 2018 was explored.  In the second phase, this same sample of 150 students was divided into two smaller samples which were people who thought lifestyle changes will or will not reduce global climate change. “Lifestyle changers” believe lifestyle changes will reduce global climate change and “non-lifestyle changers” do not believe lifestyle will reduce global climate change.  There are 89 students who believe lifestyle changes can reduce global climate change and 61 students do not believe that lifestyle changes can reduce global climate change.  On this phase of the report, attention will be given to students opinions on if they think lifestyle changes will reduce global 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 feel that lifestyle changes will reduce global 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 feel as though lifestyle changes will reduce global climate change.

 

Second, the sample results will also be used to determine if the opinion of the population of all students who believe lifestyle changes will reduce global climate change and students who do not believe lifestyle changes will reduce global climate change at Flagler College have a statistically significant difference of opinion regarding their understanding of global environmental issues.  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 who believe lifestyle changes will reduce global climate change and students who do not believe lifestyle changes will reduce global climate change with their understanding of global environmental issues.

 

Hypothesis Test #1 – A Claim of Majority

 

In the sample of 150 students, 89 reported that lifestyle changes cannot reduce global climate change. That is, the majority, 40.67% of the students sampled expressed that they do feel as though lifestyle changes can reduce global climate change.  These sample results will be used to test the claim that the majority of the population of Flagler College students who do not think that lifestyle changes can reduce global climate change at a level of significance of 0.05.  A pie chart of the data is given below.

 

Result 1: Pie Chart With Summary- Global Climate Change

 

Result 1: Pie Chart With Data-PHASE 2   [Info]
Right click to copy

 

Hypothesize

 

Null: Fifty percent of all Flagler College students believe that lifestyle changes can reduce global climate change.

 

Alternate: More than 50% of all Flagler College students believe that lifestyle changes cannot reduce global climate change.

 

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

 

Prepare

 

1. Random Sample – 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 2: One sample proportion summary hypothesis test- Lifestyle changes

 

 

Result 2: One sample proportion summary hypothesis test PIE CHART-PHASE 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
p611500.406666670.040824829-2.28619040.9889

 

Interpret

 

Since the p-value (0.9889) is more than the level of significance of 0.05, the null hypothesis must not be rejected. Therefore, there is not sufficient evidence to support the claim that the majority of all Flagler College students feel that lifestyle changes will reduce global climate change.

 

Confidence Interval #1 – Estimating the Population Proportion

 

The hypothesis test does not give sufficient evidence that the majority of all Flagler College students feel that lifestyle changes will reduce global climate change.  However, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe lifestyle changes will reduce global climate change. 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.  Moreover, 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)(0.4067) = 61 > 10 and n*(1 – phat) = (150)(1 – 0.4067) = (150)(0.5933) = 89 > 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 approximately 2500 students.

 

Result 3: One sample proportion summary confidence interval- Lifestyle changes

 

 

Result 3: One sample proportion summary confidence intervalPIECHART-PHASE 3   [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
p611500.406666670.0401072640.340696090.47263724

 

Interpret

 

We are 90% confident that between 34% and 47% of all Flagler College students find that believe lifestyle changes can reduce global climate change. This is the majority of Flagler College students, though it is very close to being equal to the minority.

 

Hypothesis Test #2 – A Claim of the Difference between two Population Proportions

 

A contingency table was created to compare the opinions of the people who believe that lifestyle changes will or will not reduce global climate change regarding their understanding of global environmental issues.  Out of the 99 lifestyle changers, 36 students felt that having an understanding of global environmental changes made them believe that lifestyle changes can reduce overall climate change and of the 51 Non-lifestyle changers, 26 felt that they do not understand global environmental changes.  That is, 0.36% (36 students out of 99) of the lifestyle changers felt having an understanding of global environmental issues and 0.51% (26 students out of the 51 students) of the Non-lifestyle changers cannot reduce global environmental issues. With an approximately 0.15% difference in these percentage, the sample gives some reason to believe that the population of lifestyle changers at Flagler College and the population of Non-lifestyle changers at Flagler College have a difference in their opinion of understanding global environmental issues.

 

Result 4: Contingency table (with data): Lifestyle Change/Understand Global Environmental Issues  

Result 4: Contingency table (with data-PHASE 2   [Info]
Contingency table results:
Rows: understand global environmental issues
Columns: Can global climate change reduce with or without lifestyle changes
NoYesTotal
No262551
Yes633699
Total8961150

Chi-Square test:
StatisticDFValueP-value
Chi-square12.23443520.135

 


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 lifestyle changers at Flagler College and the proportion of the population of Non-lifestyle changers at Flagler College who have an understanding about global environmental changes.

 

Alternate: There is a difference in the proportion of the population of lifestyle changers at Flagler College and the proportion of the population of Non-lifestyle changers at Flagler College who have an understanding about global environmental changes.

 

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) = (26 + 63)/(51 + 91) = 89/142 = 0.63

 

Sample One (lifestyle changers): Since n1*p-hat = (51)(0.63) = > 32.13 and

 

n1*(1 - p-hat) = (51)(1 – 0.63) = (51)(0.37) = 18.87 > 10, sample one is large.

 

Sample Two (non-lifestyle changers): Since n2*p-hat = (91)(0.63) = 57.33 > 10 and

 

n2*(1 - p-hat) = (91)(1 – 0.63) = (91)(0.37) = 33.67 > 10, sample two is large.

 

2. Random Samples – 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 lifestyle changers and Non-lifestyle changers.

 

 

 

 

 

Result 5: Two sample proportion summary hypothesis test- lifestyle changes/understanding global environmental issues

 

 

Result 5: Two sample proportion summary hypothesis test#2-PHASE3   [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 - p2255136990.126559710.08466651.49480270.135

 

Since the p – value = 0.135 is more than the level of significance of 0.05, the null hypothesis will be supported and not be rejected, therefore, there is sufficient evidence that there exists a difference in the proportion of the population of lifestyle changers at Flagler College and the proportion of the population of Non-lifestyle changers at Flagler College who have an understanding of global environmental changes

 

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 students understanding of global environmental changes between the population of lifestyle changers and non-lifestyle changers here 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 – Probably not, however, 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 (Lifestyle changers): Since n1*p-hat1 = (51)(0.168) = 85.68 > 10 and

 

n1*(1 - p-hat1) = (77)(1 – 0.168) = (77)(0.832) = 64.06 > 10, sample one is large.

 

Sample Two (Non-lifestyle changers): Since n2*p-hat2 = (99)(0.168) = 16.63 > 10 and

 

n2*(1 - p-hat2) = (99)(1 – 0.168) = (99)(0.832) = 82.37 > 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 are or are not affected by the opinion of lifestyle changes, we will assume 50% are and 50% are not.  There are approximately (0.50)(2500) = 1250 students who are Lifestyle changers and (0.50)(2500) = 1250 students who are Non-lifestyle changers in the population.

 

Population One (Lifestyle changers): Since 10n1 = (10)(99) = 990 < 1250, population one is big. 

 

Population Two (Non-lifestyle changers): Since 10n2 = (10)(51) = 510 < 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 6: Two sample proportion summary confidence interval- life changes/understanding of global environmental changes


Result 6: Two sample proportion summary confidence interval#2-PHASE 3   [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 - p2255136990.126559710.085073497-0.0401812760.29330071


 

Interpret

 

This confidence interval is negative on the lower limit and positive on the upper limit; this indicates that the percentage of the population of all lifestyle changers who feel that their understanding of global environmental issues is less than the percentage of the population of all Non-lifestyle changers who have an understanding of global environmental changes. Thus, I am 95% confident that the percentage of all lifestyle changers who have an understanding of global environmental changes is between 4.01% and 29.3% less than the percentage of all Non-lifestyle changers who have an understanding of global environmental changes.

 

Conclusion

 

Having an understanding on global environmental changes can be very crucial to determining what can help reduce those changes.  In this report, the sample provided evidence that the majority of all Flagler College students found that you can have an understanding of global climate change. Furthermore, it was found that there is statistical evidence that students who have an understanding of global environmental changes who believe that lifestyle changes can reduce overall global climate change are more likely to think that lifestyle change can reduce global climate change.  It was estimated that between 4.01% and 29.3% is less than the percentage of all Non-lifestyle changers who have an understanding of global environmental changes.  Since these students believe that lifestyle changes can reduce overall global climate change it would make sense that they have an understanding of global environmental issues.

 

 

 

Data set 1. Flagler College Students views on Global Warming a   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=78307">Phase Three: Flagler College Students views on Global Warming and Climate Change</A>

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