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Created: Dec 6, 2018
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Phase 3: JUUL use with Students at Flagler college
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Introduction:


In the first phase of this project, we explored the JUULing habits of a sample of 150 Flagler College Students. In the second phase, these same 150 Flagler College Students were divided into two smaller groups, Students that believed JUULs should be banned on campus (Banners) and Students who do not believe JUULs should be banned on campus (Allowers). 83 students (55.33%) believed JUULs should not be banned and 67 students (44.67%) believe JUULs should be banned. A pie chart is shown below representing this data.

Result 1: Should JUULs be Banned on FC Campus?   [Info]
Right click to copy

 


On this phase of the report,attention will be given to the opinion of the students whether they believe fruit JUUL flavors are less harmful than tobacco flavors.


First, methods of statistical inference will be used to determine if the sample results indicate if the majority of the population believe fruit flavors are more harmful than tobacco flavors. A hypothesis test will be run to find statistical evidence of majority and then a confidence interval will be created to estimate the percentage of the Flagler College Student population who feel fruit JUUL flavors are less harmful than tobacco JUUL flavors.


Second, the sample results will also be used to determine if the opinion of the population of Banners and the population of all Allowers at Flagler College have a statistically significant difference of opinion regarding the are fruit flavor less harmful than tobacco flavors. 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 Banners and Allowers who think fruit flavors are less harmful than tobacco flavors.


Hypothesis Test #1 – A Claim of Majority


In the sample of 150 students, 113 reported that fruit flavored pods are not less harmful than tobacco flavored pods. That is, the majority, 75.33%, of the students sampled expressed that fruit flavored pods are not less harmful than tobacco flavored pods. These sample results will be used to test the claim that the majority of the population of Flagler College students believe that fruit flavored pods are not less harmful than tobacco flavored pods at a level of significance of 0.05. A pie chart of the data is given below.


Result 2: Pie Chart With Data – Are fruit flavors more harmful?

 

Result 2: fruit/tobacco   [Info]
Right click to copy

 


Hypothesize

              Null: Fifty percent of all Flagler College students believe that fruit flavored pods are not less harmful than tobacco flavored pods.


              Alternate: More than 50% of all Flagler College students believe that fruit flavored pods are not less harmful than tobacco flavored pods.

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 – Less Harmful?

 

Result 3: One sample proportion summary hypothesis test- Less Harmful?   [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
p1131500.753333330.0408248296.205374<0.0001

 


Since the p-value (<0.0001) is less than the level of significance of 0.05, the null hyposthesis must be rejected. Therefore. there is suffiecent evidence to support the claim that majority of all Flagler College Student feel that fruit flavoured JUULs are not less harmful than tobacco flavours.


Confidence Interval #1 – Estimating the Population Proportion

 

              The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that fruit flavored pods are not less harmful than tobacco flavored pods. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that fruit flavored pods are not less harmful than tobacco flavored pods. 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)(0.7533) = 113> 10 and n*(1 – phat) = (150)(1 – 0.7533) = (150)(0.2467) = 37 > 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 – Less Harmful?

Result 4: One sample proportion summary confidence interval-Less Harmful?   [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
p1131500.753333330.0351968010.695439750.81122692

 


Interpret


We are 90% confident that between 69.5% and 81.1% of all Flagler College students find that fruit flavored pods are not less harmful than tobacco flavored pods. 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 whether or not students believed JUULs should be banned and if they believed that fruit flavour JUUL pods were less harmful compared to tobacco. Of the 67 students who believe that JUULs shouldn’t be banned, 56 did not think that fruit flavours are less harmful than tobacco and of the 83 students who believe that JUULs should be banned, 57 did not think that fruit flavours are less harmful than tobacco. That is, 83.6% (56 out of 67 students) of the No, Banned on FC Campus felt that fruit flavours were less harmful and 68.7% (57 out of 83 students) of the Yes, Banned on FC Campus felt that fruit flavours were less harmful. With a 14.9% difference in these percentages, the sample gives reason to believe that the population of No, Banned on FC Campus and the population of Yes, Banned on FC Campus differ in their opinion that fruit flavours are not less harmful than tobacco.


Result 5: Contingency table (with data)- Banners vs. Less Harmful

Result 5: comparison 3.1   [Info]
Contingency table results:
Rows: Banned on FC Campus
Columns: Less Harmful
NoYesTotal
No, Banned561167
Yes, Allowed572683
Total11337150

Chi-Square test:
StatisticDFValueP-value
Chi-square14.43370970.0352

 

 

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 No, Banned on FC Campus and the proportion of the population of Yes, Banned on FC Campus that believe that fruit flavours are not less harmful than tobacco.

Alternate: There is a difference in the proportion of the population of No, Banned on FC Campus and the proportion of the population of Yes, Banned on FC Campus that believe that fruit flavours are not less harmful than tobacco.

 

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) = (56 + 57)/(67 + 83) = 113/150 = 0.7533

 

Sample One (Banners): Since n1*p-hat = (67)(0.7533) = 50.747 > 10 and

 

n1*(1 - p-hat) = (67)(1 – 0.7533) = (67)(0.2467) = 24.67 > 10, sample one is large.

 

Sample Two (Allowers): Since n2*p-hat = (83)(0.7533) = 62.524 > 10 and

 

n2*(1 - p-hat) = (83)(1 – 0.7533) = (83)(0.2467) = 20.5 > 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 No, Banned and Yes, Banned

 

Compute

 

Result 6: Two Sample proportion summary hypothesis test- Banners vs. Less Harmful 

Result 6: Two sample proportion summary hypothesis test (result6)   [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 - p2566757830.149073910.0707975142.10563760.0352

 

Interpret:

Since the p-value = 0.0352 is less than the level of significance of 0.05, the null hypothesis will rejected. Therefore, there is sufficient evidence that exists a difference in the proportion of the population of No, Banned and the proportion population of Yes, Banned who believe that fruit flavours are not less harmful than tobacco.

 

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 fruit flavours are not less harmful than tobacco between the population of No, Banned and Yes, Banned. 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 90% 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 (Banners): Since n1*p-hat1 = (67)(0.836) = 56 > 10 and

 

n1*(1 - p-hat1) = (67)(1 – 0.836) = (67)(0.164) = 11 > 10, sample one is large.

 

Sample Two (Allowers): Since n2*p-hat2 = (83)(0.687) = 57 > 10 and

 

n2*(1 - p-hat2) = (83)(1 – 0.687) = (83)(0.313) = 26 > 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 students who believe fruit flavored pods are not less harmful than tobacco flavored pods, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Social Students and (0.50)(2500) = 1250 students who are Unsocial Students in the population.

 

Population One (Social Students): Since 10n1 = (10)(67) = 670 < 1250, population one is big.

 

Population Two (Unsocial Students): Since 10n2 = (10)(83) = 830 < 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- Banners vs. Less Harmful

Result 7: Two sample proportion summary confidence interval (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

90% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p2566757830.149073910.0681175350.0370305340.26111728

 

Interpret

 

This confidence interval is completely negative; this indicates that the percentage of the population of all Banners who feel fruit flavours are less harmful than tobacco is not less than the percentage of the population of all Allowers who feel fruit flavours are not less harmful than tobacco.  Thus, I am 90% confident that the percentage of all students who believe that fruit flavours are not less harmful than tobacco is between 3.7% and 26.11%.



Conclusion

JUULing is continuously becoming a more prevalent topic in today’s society and understanding people’s knowledge of JUUL products is an important topic. In this report, the sample provided evidence that the majority of all Flagler College students believe fruit flavors are not less harmful than tobacco flavors. In fact, it was estimated that between 69.5% and 81.1% of all Flagler College students believe that fruit flavors are not less harmful than tobacco flavors.  Furthermore, it was found that there is not statistical evidence that the proportion of Banners who believe fruit flavors are less harmful is less than the Allowers who believe fruit flavors are less harmful. It was estimated that between 3.7% and 26.11% of all students who believe that fruit flavours are not less harmful than tobacco. This is a natural association because the Allowers are more knowledgeable regarding JUUL products and they are aware fruit flavors are not less harmful than tobacco flavors.  

 

JUUL is an upcoming societal issue especially within the college student population.  Hence, it is surprising majority of students do not know all flavors are equally as harmful.  Maybe increasing awareness of JUUL products and what they do to the body will also increase the proportion of people who are knowledgeable about the JUUL products. People know JUULs exist. Many surveys show people have seen other students JUUL on campus, people know other friends who use JUUL products frequently, and many people use JUUL products themselves. Although, there is no shown difference between Banners and Allowers knowledge on the harmful effects based on flavors, increasing awareness will better everyone’s understanding as a population.

Data set 1. Flagler College Students and JUUL - Carr, Figueroa   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82713">Phase 3: JUUL use with Students at Flagler college</A>

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