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Phase Three: Driver Safety of Flagler students in Fall 2018

Phase Three: Driver Safety of Flagler students in Fall 2018

Introduction

For the first phase of the project, the Driving tendencies of 150 Flagler students in the Fall semester of 2018 were analyzed. In the second phase of the project students were divided into “Course” and “No Course”, based on whether they took a drivers education course or did not take a drivers education course. The “Course students” are the ones who have taken a driver’s education course, and the “No Course” have not taken a driver’s education course. There are 88 Course students and 62 No Course students.  A bar chart representing the two samples is presented below.

Result 1: Bar Graph No Course and Course Students Sampled   [Info]

On this phase of the report we will analyze how whether or not Flagler students think it is safe to drive while holding and talking on your cell phone.

We will be using methods of statistical inference to determine if the sample results will indicate that the majority of the population of all Flagler students think it is safe to drive while talking or holding your cell phone. A hypothesis test will find evidence of the majority and a confidence interval will be made to estimate the percentage of the population who believe it is unsafe to drive while talking on or holding your cell phone. The sample results collected will determine if the opinions of the population of all Flagler students have a statistically significant difference of opinion, regarding using your cell phone while driving. Finding statistical evidence of a difference will once again rely on the hypothesis test, while creating a confidence interval will estimate the difference in percentage of the population of Course and No-Course students who utilize or hold their phone while driving.

Hypothesis Test #1- A Claim of Majority

Of the sample of 150 students, 131 of them reported that talking on a cellphone while driving is not safe. This means that the majority of students sampled, 87.33%, feel that talking on a phone while driving is unsafe. These sample results will be used to test the claim that the majority of the population of Flagler College students also view talking on a cellphone while driving as an unsafe practice, at a level of significance of 0.05. A pie chart of the data is given below:

Result 2: Talking on the Phone While Driving - Is It Safe (All)   [Info]

Hypothesize

Null:  Fifty percent of all Flagler College students believe that talking on the phone while

driving is unsafe

Alternate:More than 50% of all Flagler College students believe that talking on the

phone while driving is unsafe.

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

Prepare

1. Random Sample – It’s likely not random but 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.  (Flagler College has a population of around 2500 students.)

4. Independence within Sample – Yes, the student responses were independent of each other.

Compute

Result 3: One sample proportion summary hypothesis test - Phone While Driving   [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
p1311500.873333330.0408248299.1447617<0.0001

Interpret

The large test statistic obtained from this hypothesis test suggests that the probability of the null hypothesis occurring is unusual. This is complemented by an extremely low p-value of less than 0.0001, which is less than the significance level of 0.05,  resulting in my group’s rejecting the null hypothesis. There is not enough evidence that suggests that half (50%) of Flagler students feel the talking on a phone while driving is dangerous. Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students feel that talking on the phone while driving is unsafe.

Confidence Interval #1- Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that talking on a cellphone while driving is an unsafe practice, therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe the same. 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 – Although it probably isn’t random, to proceed, we will assume it is; The student responses were independent of each other.

2.Large Sample – Since n*phat = (150)(0.8733) = 130 > 10 and n*(1 – phat) = (150)(1 – 0.8733) = (150)(0.1267) = 19 > 10, the sample is large.

3.Big Population – Since 10n = (10)(150) = 1500 < 2500, the population is big. Flagler College has a population of around 2500 students.

Compute

Result 4: One sample proportion summary confidence interval 90%   [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
p1311500.873333330.027156610.828664680.91800198

Interpret

We are 90% confident that between 82.9% and 91.8% of all Flagler College students feel that talking on the phone while driving is unsafe. This is clearly the majority of all Flagler College students.

Hypothesize Test #2-  A Claim of the Difference between two Population Proportions

A contingency table was created to compare the opinions of the Course and No Course students regarding if they used their cell phone while driving. There are 62 No Course students and 88 Course students. Out of the 62 No Course students, only 5 of them said yes they do use their cell phones while driving. While the remaining 57 No Course students said no, they do not use their cell phone while driving. For the 88 Course students, 74 of them said no they did not use their cell phones while driving, while 14  Course students said yes, they do. Therefore, out of the total 150 students, only 19 students said yes, they used their cell phones while driving.

### Contingency table results:

Rows: Driver Education

Columns: Talking on Cell Phone while Driving

 No Yes Total No 57 5 62 Yes 74 14 88 Total 131 19 150

### Chi-Square test:

 Statistic DF Value P-value Chi-square 1 2.0233897 0.1549

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. A 95% confidence interval was created.

Hypothesize

Null: There is not a substantial difference between the population of Course students at Flagler and the proportion of the population of No Course students at Flagler college who believe.

Alternate:There is a substantial difference in the proportion of the population of Course students at Flagler College and the proportion of the population of No Course students at Flagler College who feel there should be a law against using a cell phone while driving.

Prepare

1. Random Sample with Independent Observations – Although it probably isn’t random, to proceed, we will assume it is; The student responses were independent of each other.

2.Large Sample – Since n*phat > 10 and n*(1 – phat) > 10, the sample is large.

3.Big Population – Since 10n = (10)(150) = 1500 < 2500, the population is big. Flagler College has a population of around 2500 students.

4. Independence within Sample – Yes, the student responses were independent of each other.

Compute

Interpret

The Hypothesis Test created was meant to give us an indication if the difference between Course and No Course students at Flagler College, was statistically significant. Since the p-value (.1549) is greater than the significance level of .05, we will fail to reject the null hypothesis.Meaning that there is not substantial evidence that there is a big difference between the Course students and No Course students.

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

The Hypothesis test gave our group enough evidence that there is significant difference in the opinions of Flagler students who have taken a driving class and those who have not. The opinion was about if a law should be in place to prevent texting and driving. A confidence interval will be created to estimate the difference and hopefully confirm that the two population proportions cannot be equal.

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 SamplesCourse students sample is greater than or equal to 10. And no Course students is also greater than or equal to 10. So

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 a drivers education course, we will assume 50% have and 50% have not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Course Students and (0.50)(2500) = 1250 students who are No course Students in the population.

Population One (Social Students): Since 10n1 = (10)(62) = 620 < 1250, population one is big.

Population Two (Unsocial Students): Since 10n2 = (10)(88) = 880< 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

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:

 Difference Count1 Total1 Count2 Total2 Sample Diff. Std. Err. L. Limit U. Limit p1 - p2 5 62 12 88 -0.055718475 0.050339949 -0.15438296 0.042946011

Conclusion