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PHASE THREE: Flagler College Students and JUULs - Erin B., Desinty Z., Skylar L.
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Introduction:

On the first phase of this project, the JUUL habits 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 Ban Students and the Allow Students.  The term “Ban Students” defined the sample of those Flagler College students who do not think JUUL should be allowed on campus and the term “Allow Students” defined the sample of those Flagler College students who do think JUUL should be allowed on campus.  There are 68 Ban Students and 82 Allow Students sampled.  A bar chart representing the two samples is presented below.

Result 1: Bar Plot With Data - Should JUULs be Banned on FC Campus   [Info]
Right click to copy

 

On this phase of the report, attention will be given to students’ opinions about JUUL being allowed on the FC campus.

 

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 JUUL should be banned.  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 JUUL should be banned.

 

Second, the sample results will also be used to determine if the opinion of the population of all Ban Students and the population of all Allow Students at Flagler College have a statistically significant difference of opinion regarding the JUUL habits that affect their everyday life.  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 Ban Students and Allow Students who find JUUL should be banned on campus.


Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 85 reported that they have previously not used JUUL at some point in their life.  That is, the majority, 56.67%, of the students sampled expressed they have not used JUUL. These sample results will be used to test the claim that the majority of the population of Flagler College students believe JUUL should not be banned at a level of significance of 0.05  A pie chart of the data is given below.

Result 2: Pie Chart With Data - Students Who Have Used JUUL   [Info]
Right click to copy


Hypothesize

              Null: Fifty percent of all Flagler College students have not experienced using a JUUL.

              Alternate: More than 50% of all Flagler College students have not experience using a JUUL.

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.


Compare

Result 3: One sample proportion summary hypothesis test - Students Who Have Used JUUL   [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
p851500.566666670.0408248291.63299320.0512

 

Interpret

Since the p-value (0.0512) is more than the level of significance of 0.05, we must fail to reject the null hypothesis.  Therefore, there is not sufficient evidence to show that there has been an increase in the majority of Flagler students who have not used a JUUL.

 

Confidence Interval #1 – Estimating the Population Proportion

              The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that social media is a distraction to their day.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that social media is a distraction to their day.  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)(0.5667) = 85 > 10 and n*(1 – phat) = (150)(1 – 0.5667) = (150)(0.4333) = 65 > 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.


Compute

Result 4: One sample proportion summary confidence interval - Students Who Have Used JUUL   [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
p851500.566666670.0404603140.500115370.63321796

 

Interpret

We are 90% confident that between 50.01% and 63.32% of all Flagler College students have not used JUUL. 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 Ban Students and Allow Students regarding them opinion of whether or not JUUL should be banned on FC campus.  Of the 68 Ban Students, 51 had never used JUUL and of the 82 Allow Students, 34 had never used JUUL.  That is, 75% (51 students out of 68) of the Ban Students never used JUUL and 41.46% (34 students out of the 82 students) of the Allow Students have never used JUUL.  With an approximately 34% difference in these percentage, the sample gives some reason to believe that the population of Ban Students at Flagler College and the population of Allow Students at Flagler College differ in whether or not they used JUUL.

Result 5: Contingency table - Ban or Allow Students VS Students Who Have Used JUUL   [Info]

Contingency table results:


Rows: Ban or Allow on FC Campus
Columns: Students Who Have Used JUUL
NoYesTotal
No, Banned511768
Yes, Allowed344882
Total8565150

Chi-Square test:


StatisticDFValueP-value
Chi-square117.026266<0.0001

 

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 Ban Students at Flagler College and the proportion of the population of Allow Students at Flagler College who use JUUL.

Alternate: There is a difference in the proportion of the population of Ban Students at Flagler College and the proportion of the population of Allow Students at Flagler College who have used JUUL.

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) = (17 + 48)/(68 + 82) = 65/150 = 0.4333

Sample One (Ban Students): Since n1*p-hat = (68)(0.5667) = 38.5 > 10 and

n1*(1 - p-hat) = (81)(1 – 0.5667) = (68)(0.4333) = 29.5 > 10, sample one is large.

Sample Two (Allowed Students): Since n2*p-hat = (82)(0.5667) = 46.5 > 10 and

n2*(1 - p-hat) = (82)(1 – 0.5667) = (81)(0.4333) = 35.1 > 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 Ban Students and the Allow Students.


Compute

 

Result 6: Two sample proportion summary hypothesis test - Ban/Allow Students Vs. Students Who Have Used JUUL   [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 - p217684882-0.335365850.081275403-4.1262897<0.0001

 

Interpret

Since the p – value = <0.001 is less 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 Ban Students at Flagler College and the proportion of the population of Allowed Students at Flagler College who use JUUL.

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 social media is a distraction between the population of Ban Students at Flagler College and the population of Allow 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 (Ban Students): Since n1*p-hat1 = (68)(0.25) = 17 > 10 and

n1*(1 - p-hat1) = (68)(1 –0.25) = (68)(0.75) = 51 > 10, sample one is large.

Sample Two (Allowed Students): Since n2*p-hat2 = (82)(0.585) = 47.97 > 10 and

n2*(1 - p-hat2) = (82)(1 – 0.585) = (82)(0.415) = 34.03 > 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 socially by social media, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Ban Students and (0.50)(2500) = 1250 students who are Allow Students in the population.

Population One (Ban Students): Since 10n1 = (10)(68) = 680 < 1250, population one is big.

Population Two (Allowed Students): Since 10n2 = (10)(82) = 820 < 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

 

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

95% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p217684882-0.335365850.075612589-0.4835638-0.1871679

 

Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all Ban Students who have used JUUL is less than the percentage of the population of all Allowed Students who have used JUUL.  Thus, we are 95% confident that the percentage of all Allowed Students who have used JUUL is between 18.7% and 48.4% less than the percentage of all Ban Students who have used JUUL.

 

Conclusion

Society has embraced JUUL’s and the consequences that it has on our daily lives as an important topic.  In this report, the sample provided evidence that the majority of all Flagler College students have not used JUUL.  In fact, it was estimated that between 18.7% and 48.4% of all Flagler College students have not used JUUL. Furthermore, it was found that there is statistical evidence that those students who feel JUUL should be banned have a larger proportion who have not used JUUL.




Data set 1. Flagler College Students and JUULS (9AM)   [Info]
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