Print - Back

Phase Three: Flagler College Students and School Shootings Spring 2019
Generated Apr 25, 2019 by mzaczek695

Introduction:

On the first phase of this project, the students in school shootings of a sample of 150 Flagler College students from fall semester 2016 was explored.  In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as whether students believe the school shooter should be executed and the students who believe the school shooter should not be executed.  The term “For Execution” defined the sample of those Flagler College students who believe the school shooter should be executed and the term “Against Executions” defined the sample of those Flagler College students who believe the school shooter should not be executed.  There are 85 “For Executed” and 65 “Against Executed” students sampled. A bar chart representing the two samples is presented below.

<result1>This report includes Flagler College Students opinion on whether a shooter should be executed or not and then the gender of the same sample.

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 a shooter should not be executed.  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 this way.

Second, the sample results will also be used to determine whether students are okay with concealment and carrying a gun on campus or not at Flagler College have a statistically significant difference between agreeing 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 between agreeing with having a gun on campus or not agreeing.

Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 120 reported that they do not think concealed weapons should be allowed on campus. That is the majority, 80% of students sampled expressed that weapons should not be concealed. These sample results will be used to test the claim that the majoirty of Flagler College students believe that weapons should not be concealed at a level of significance of 0.05. A pie chart of the data is given below.

<result2>Hypothesize

Null: Fifty percent of all Flagler College students believe that there should not be concealed weapons on campus.

Alternate: More than 50% of all Flagler College students believe that there should not be concealed weapons on campus

Based on the alternate hypothesis, this is a left-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.

<result3>Interpret Since the p-value (<0.0001) 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 feel that social media is a distraction to their day.

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)(0.7133) = 107 > 10 and n*(1 – phat) = (150)(1 – 0.7133) = (150)(0.2867) = 43 > 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

<result4> Interpret We are 90% confident that between 74.6% and 85.4% of all Flagler College students find that you should not have concealed weapons on campus.  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 Students who believe a school shooter should be executed and the Students who are against the execution of school shooters regarding if they are for or against concealed weapons on campus. Of the 85 Students who are against execution, 73 did not support concealed weapons on campus and of the 65 Students who support the execution of a school shooter, 47 did not support concealed weapons on campus.  That is, 85.9% (73 students out of 85) of the Students who are against the execution of a school shooter felt that students should not conceal and carry weapons on campus and72.3% (47 students out of the 65 students)of the Students who support the execution of a school shooter felt that students should not conceal and carry weapons on campusWith an approximately 14% difference in these percentage, the sample gives some reason to believe that the populationstudents who support the execution of a school shooter and students who are against the execution at Flagler College differ in their opinion that students should be able to conceal weapons on campus.

<result5>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 people who think shooters should not be executed at Flagler College and the proportion of the population of Flagler College students who are against concealing and carrying a gun on campus.

Alternate: There is a difference in the proportion of the population of students who think shooters should not be executed at Flagler College and the proportion of the population of Flagler College students who are against concealing and carrying a gun on campus.

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) = (65+120)/(150+150) = 185/300= 0.6167

Sample One (Executions): Since n1*p-hat = (65)(0.7133) = 46.3645 > 10 and

n1*(1 - p-hat) = (65)(1 – 0.7133) = (65)(0.2867) = 18.6355 > 10, sample one is large.

Sample Two (Unsocial Students): Since n2*p-hat = (120)(0.7133) = 85.596 > 10 and

n2*(1 - p-hat) = (120)(1 – 0.7133) = (120)(0.2867) = 34.404 > 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 concealment of guns on campus and whether or not the students felt the should execute the shooter or not

<result6>Interpret

Since the p – value <0.0001 is less than the level of significance of 0.05, the null hypothesis will be rejected. Therefore, there is sufficient evidence that there is a difference of the population of students who think shooters should not be executed at Flagler College and the proportion of the population of Flagler College students who are against concealing and carrying a gun on campus.

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 shooters should be/should not be executed between the population of  students who are for/against carrying a gun on campus 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 (Social Students): Since n1*p-hat1 = (65)(0.593) = 38.545  > 10 and

n1*(1 - p-hat1) = (65)(1 – 0.593) = (65)(0.407) = 26.455  > 10, sample one is large.

Sample Two (Unsocial Students): Since n2*p-hat2 = (120)(0.855) = 102.6 > 10 and

n2*(1 - p-hat2) = (120)(1 – 0.855) = (65)(0.145) = 17.4 > 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 agree with executing a shooter, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are against execution and (0.50)(2500) = 1250 students who are against concealing a gun on campus.

Population One (Social Students): Since 10n1 = (10)(65) = 650 < 1250, population one is big.

Population Two (Unsocial Students): Since 10n2 = (10)(120) = 1200< 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.

<result7> Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all students who don’t agree with executions and agree with having guns on campus less than the percentage of the population of all students who agree with executions and are against concealing and carrying a gun on campus.  Thus, I am 95% confident that students who agree with executions and are against concealing and carrying a gun on campus is between 26.5% and 46.9% greater than the percentage of students who don’t agree with executions and agree with having guns on campus.

Conclusion

Our topics is important in today’s society because of the amount of shootings at schools is rising. A student’s opinion is important so they feel safe with certain regulations such as not being allowed to have a gun on campus and/or executing someone if they were to shoot. In this report, the sample provided evidence that the majority of all Flagler College students want a shooter executed.  In fact, it was estimated that between 74.6% and 85.4% of all Flagler College students find that you should not have concealed weapons on campus. .Furthermore, it was found that there is statistical evidence that those students who want a shooter executed also do not want guns on campus. This is probably largely due to if a student is uneasy with guns, they also are opinionated on what happens to a shooter (execution).

It is interesting that that majority of students are not okay with guns on campus yet there are still around a quarter of the sampled students who think concealing and carrying is a good option. This is interesting because if the majority of shooters should be executed, then why should guns be allowed on a campus at all?

Result 1: Result 1: Executions   [Info]

Result 2: Result 2: Concealment   [Info]

Result 3: Result 3: Hypothesis Test   [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
p1201500.80.0408248297.3484692<0.0001

Result 4: 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
p1201500.80.0326598630.746279310.85372069

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

### Contingency table results:

Rows: Executed
Columns: Concealed Weapons
NoYesTotal
No731285
Yes471865
Total12030150

### Chi-Square test:

StatisticDFValueP-value
Chi-square14.24208140.0394

Result 6: Result 6: Two sample proportion summary hypothesis test   [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
p1201500.80.0408248297.3484692<0.0001

Result 7: 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 - p265150120150-0.366666670.051997151-0.46857921-0.26475412