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Created: Dec 7, 2018
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Peterson PHASE THREE: Social Media Habits of Flagler College Students in Fall 2018
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Introduction

On the first phase of this project, the students and driver safety of Flagler College Students

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. The two samples include: the sample of Flagler College students who have taken driver’s education and the sample of Flagler College students who have not taken driver’s education. There are 62 students who did not take driver’s education and 88 students who did take driver’s education.

There are 62 students who did not take driver’s education and 88 students who did take driver’s education.


 


On this phase of the report, attention will be given to students’ who text and drive.

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 text and drive. 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 who text and drive Second, the sample results will also be used to determine if the opinion of the population of all Flagler College students who have taken driver’s education and the sample of Flagler College students who have not taken driver’s education have a statistically significant difference of opinion regarding texting while driving.  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 of Flagler College students who have taken driver’s education and the sample of Flagler College students who have not taken driver’s education.


Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 143 reported that they don’t text and drive. That is, the majority, 95.33%, of the students stated that they do not text while driving. These sample results will be used to test the claim that the majority of the population of Flagler College students do not text while driving at a level of significance of 0.05  A pie chart of the data is given below.


 


Hypothesize

              Null: Fifty percent of all Flagler College students do not text while driving.

              Alternate: More than 50% of all Flagler College students do not text while driving.

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 < 2600, the population is big.  Recall, Flagler College has a population of appropriately 2600 students.

              4. Independence within Sample – Yes, the student responses were taken in such a way that their responses were independent of each other.

Compute


 


Since the p-value (

Confidence Interval #1 – Estimating the Population Proportion

              The hypothesis test gives sufficient evidence that the majority of all Flagler College students do not text while driving. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who do not text while driving.  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)(0.9533) = 142.995 > 10 and n*(1 – phat) = (150)(1 – 0.9533) = (150)(0.0467) = 7/005 > 10, the sample is not 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




Interpret

We are 90% confident that between 92.5% and 98.2% of all Flagler College students do not text while driving. 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 whether students who had taken driver’s education and those who have not regarding whether or not they text while driving.  Of the 88 students who had taken driver’s education 4 admitted to texting while driving, and of the 62 students who had not taken driver’s education 3 admitted to texting while driving. That is, 4.5% (4 students out of 88) of the students who had taken driver’s education text while driving and 4.8% (3 students out of the 62 students) of the students who had not taken driver’s education text while driving..  With an approximately .3% difference in these percentage, the sample gives little reason to believe that the population of students have taken driver’s education differ in their frequency of texting while driving.


 


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 who have taken driver’s education at Flagler College and the proportion of the population of students who have not taken driver’s education at Flagler College who text while driving.

Alternate: There is a difference in the proportion of the population of who have taken driver’s education at Flagler College and the proportion of the population of students who have not taken driver’s education at Flagler College who text while driving.

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) = (4 + 3)/(88 + 62) = 7/150 = .0467

Sample One (Have taken driver’s ed): Since n1*p-hat = (88)(0.0467) = 57.8 < 10 and

n1*(1 - p-hat) = (88)(1 – 0.0467) = (88)(0.9533) = 83.9 > 10, sample one is not large.

Sample Two (Unsocial Students): Since n2*p-hat = (62)(0.0467) = 2.9 < 10 and

n2*(1 - p-hat) = (62)(1 – 0.0467) = (62)(0.9533) = 59.1 > 10, sample two is not 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 students who have taken driver’s education and the students who have not.

 

Compute




Interpret

Since the p – value = 0.9332 is more than the level of significance of 0.05, the null hypothesis will not be rejected.  Therefore, there not is sufficient evidence that there exists a difference in the proportion of the population of Students at Flagler College who have taken driver’s

education and the proportion of the population of Flagler College Students who have not taken driver’s education who text while driving.

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 amount of students who text and driver between the population of Students at Flagler College who have taken driver’s education and the population of Students at Flagler College who have not taken driver’s education. 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 – It is found that the pooled sample proportion is

 

p-hat = (x1 + x2)/(n1 + n2) = (4 + 3)/(88 + 62) = 7/150 = .0467

Sample One (Have taken driver’s ed): Since n1*p-hat = (88)(0.0467) = 57.8 < 10 and

n1*(1 - p-hat) = (88)(1 – 0.0467) = (88)(0.9533) = 83.9 > 10, sample one is not large.

Sample Two (Unsocial Students): Since n2*p-hat = (62)(0.0467) = 2.9 < 10 and

n2*(1 - p-hat) = (62)(1 – 0.0467) = (62)(0.9533) = 59.1 > 10, sample two is not 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 have or have not taken driver’s education, we will assume 50% have and 50% have not.  Hence, there are approximately (0.50)(2500) = 1250 students who have taken driver’s education and (0.50)(2500) = 1250 students who have not taken driver’s education in the population.

Population One (students who have taken driver’s ed): Since 10n1 = (10)(88) = 880 < 1250, population one is big.

Population Two (students who have not taken driver’s ed): Since 10n2 = (10)(62) = 620 < 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

 



Interpret

This confidence interval includes 0; this indicates that the percentage of the population of all Students who have taken driver’s education could be the same percentage as those students who have not taken driver’s education. Since the confidence interval contains 0, we can conclude there is no significant statistical difference in the proportion of students who have taken and those who have not that text and drive.

 

Conclusion

Following Hypothesis test #1 and hypothesis test #2 we can now state that the hypothesis test did not give us sufficient evidence that there is a significant difference in the amount of students who text and drive between the population of Students at Flagler College who have taken driver’s education and the population of Students at Flagler College who have not taken driver’s education Since a two tailed test with a level of significance of 0.05 was run, a 95% confidence interval will be created. In the sample of 150 students, 143 reported that they don’t text and drive. That is, the majority, 95.33%, of the students stated that they do not text while driving. These sample results will be used to test the claim that the majority of the population of Flagler College students do not text while driving at a level of significance of 0.05. We are 90% confident that between 92.5% and 98.2% of all Flagler College students do not text while driving. This is certainly the majority of all Flagler College students. In today’s society texting and driving is a very big safety hazard and it is very good that the majority of Flagler College Students do not text and drive.



 

Result 1: Bar Plot With Data   [Info]
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Result 2: Pie Chart With Data   [Info]
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Result 3: One sample proportion summary hypothesis test - don't text   [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
p1431500.953333330.04082482911.104354<0.0001

Result 4: One sample proportion summary confidence interval   [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
p1431500.953333330.0172218640.925005890.98166078

Result 5: Contingency table (with data)   [Info]
Contingency table results:
Rows: Driver Education
Columns: Text while Driving
NoYesTotal
No59362
Yes84488
Total1437150

Chi-Square test:
StatisticDFValueP-value
Chi-square10.00703109210.9332
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Result 6: Two sample proportion summary hypothesis test   [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 - p2488362-0.00293255130.034973108-0.0838516070.5334

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 - p2488362-0.00293255130.03515287-0.0718309110.065965809

Data set 1. Flagler College Students and Driver Safety - Aguer   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82860">Peterson PHASE THREE: Social Media Habits of Flagler College Students in Fall 2018</A>

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