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PHASE THREE: Flagler College Students and Climate Change in Spring 2019
Generated Apr 26, 2019 by cgblades

On the first phase of this project, the beliefs of 100 Flagler College students from fall semester 2016 on whether or not climate change is real or not was explored.  In the second phase, this same sample of 100 students was divided into two smaller samples which were referred to as the Coastal Students and the Noncoastal Students.  The term “Coastal Students” defined the sample of those Flagler College students who live near the  coast and the term “Noncoastal Students” defined the sample of those Flagler College students who do not live near the coast.  There are 59 Coastal Students and 41 Noncoastal Students sampled.  A bar chart representing the two samples is presented below.

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

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 noncoastal Students at Flagler College have a statistically significant difference of opinion regarding the belief that climate change is real or not. 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 Noncoastal Students who believe that climate change is real.

Hypothesis Test #1 – A Claim of Majority

In the sample of 100 students, 94 reported that climate change is real to their day.  That is, the majority, 94% of the students sampled expressed that they believe 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 climate change is real at a level of significance of 0.05  A pie chart of the data is given below.

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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 = (100) (0.50) = 50 > 10 and n(1-p0) = (100) (0.50) = 50 > 10 are both true statements, the sample is large.

3. Big Population – Since 10n = (10)(100) = 1000 < 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

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Interpret

Since the p-value (<0.0359) 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 believe 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 believe 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 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 = (100)(0.59) = 59 > 10 and n*(1 – phat) = (100)(1 – 0.59) = (100)(0.41) = 41 > 10, the sample is large.

3. Big Population – Since 10n = (10)(100) = 1000 < 2500, the population is big.  Recall, Flagler College has a population of appropriately 2500 students.

Compute

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Interpret

We are 90% confident that between 50.9% and 67.1% of all Flagler College students find that social media is a distraction to their day.  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 Noncoastal Students regarding the belief that climate change is real.  Of the 41 Noncoastal Students, 39 believed climate change was real and of the 69 Coastal Students, 59 believed that climate change was real.  That is, 95.1% (39students out of 41) of the Noncoastal students believed that climate change was real and 93.2% (55 students out of the 59 students) of the Coastal Students believed social media was real.  With an approximately 2% difference in these percentage, the sample gives some reason to believe that the population of coastal Students at Flagler College and the population of noncoastal Students at Flagler College do not differ in their opinion of whether or not climate change is real.

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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 Noncoastal 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 Noncoastal Students at Flagler College who feel social media is a distraction.

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) = (39 + 55)/(41 + 59) = 94/100 = .94

Sample One (NonCoastal Students): Since n1*p-hat = (41)(0.59) = 24.19 > 10 and

n1*(1 - p-hat) = (41)(1 – 0.59) = (41)(0.41) = 16.81 > 10, sample one is large.

Sample Two (Coastal Students): Since n2*p-hat = (59)(0.59) = 34.81 > 10 and

n2*(1 - p-hat) = (59)(1 – 0.59) = (69)(0.41) = 28.29 > 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 Noncoastal Students.

Compute

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Interpret

Since the p – value = 0.6937 is greater than the level of significance of 0.05, the null hypothesis will fail to reject.  Therefore, there is sufficient evidence that there is no difference in the proportion of the population of Coastal Students at Flagler College and the proportion of the population of Noncoastal Students at Flagler College who believe that climate change is real.

Confidence Interval #2 –Estimate the Difference between two Population Proportions

The hypothesis test gave us sufficient evidence that there is not a significant difference in the belief that climate change is real between the population of Coastal Students at Flagler College and the population of Noncoastal Students at Flagler College. Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions are 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 (Noncoastal Students): Since n1*p-hat1 = (39)(0.951) = 37 > 10 and

n1*(1 - p-hat1) = (39)(1 – 0.951) = (39)(0.049) = 2 > 10, sample one is large.

Sample Two (Coastal Students): Since n2*p-hat2 = (55)(0.932) =51 > 10 and

n2*(1 - p-hat2) = (55)(1 – 0.932) = (55)(0.068) = 4 > 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 do or do not believe in climate change, 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 Coastal Students in the population.

Population One (Noncoastal Students): Since 10n1 = (10)(41) = 410 < 1250, population one is big.

Population Two (Coastal Students): Since 10n2 = (10)(59) = 590 < 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.

Compute

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Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all Noncoastal Students believe climate change is real is less than the percentage of the population of all Coastal Students who believe climate change is real.  Thus, I am 95% confident that the percentage of all Coastal Students who believe climate change is 2% greater than the percentage of all Noncoastal students who feel social media is a distraction.

Conclusion

Climate change is a controversial topic, but where we live in the world might play a role in how we view the topic. In this report, the sample provided evidence that the majority of all Flagler College students find climate change to be real.  In fact, it was estimated that between 93% and 95% of all Flagler College students believe that climate change is real.  Furthermore, it was found that there is little statistical evidence that those students who live in coastal areas have a greater believe that climate change is real than those who live  in  noncoastal areas. It was estimated that there was a 2% difference in the beliefs of all Flagler College students who lived in coastal areas and believed and of those who didn’t.  This is natural association to me.  I feel that climate change is becoming more and more well known, because more facts and data is coming out about how quickly the climate is changing. I now know I am not alone.

It is interesting that there was not that big of a difference. However, those living in a coastal region had a 2% higher belief than those who didn’t.  I think that because climate change is such a talked  about subject it is making students think more about it.

Result 1: Survey of Students Who Are From a Coastal Region   [Info]

Result 2: Pie Chart With Data-climate change real   [Info]

Result 3: One sample proportion summary hypothesis test-students from a coastal region   [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
p591000.590.051.80.0359

Result 4: One sample proportion summary confidence interval-survey of students from a coastal region   [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
p591000.590.0491833310.509100620.67089938

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

Contingency table results:

Rows: Coastal Region
Columns: Is Climate Change real
NoYesTotal
No23941
Yes45559
Total694100

Chi-Square test:

StatisticDFValueP-value
Chi-square10.155096030.6937
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Result 6: Two sample proportion summary hypothesis test-HT #2   [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 - p2394155590.0190161220.0482860430.393822340.6937

Result 7: Two sample proportion summary confidence interval-CI #2   [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 - p2394155590.0190161220.046935284-0.0729753430.11100759