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Created: Apr 26, 2019
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Phase 3: School Shootings
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Introduction:

On the first phase of this project, the opinions of weather or not school shooters should be executed 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 categorized as executed and not not executed. The term “executed” defined the sample of those Flagler College students who believe school shooters should be executed and “not executed” represents students who believe school shooters should not be executed. 83 students responded with no school shooters should not be executed and 63 students responded with yes, school shooters should be executed.  A bar chart representing the two samples is presented below.

Result 1: Bar Plot With Data-Should School Shooters be Executed? *with value*   [Info]
Right click to copy


Result 1: Public School and Not Public School Students Sampled


On this phase of the report, attention will be given to students’ opinions about whether school shooters should be executed or not.

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 school shooters should 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 school shooters should be executed.


Second, the sample results will also be used to determine if the opinion of the population of all Not Public School Students and the population of all Public Schooled Students at Flagler College have a statistically not significant difference of opinion regarding the punishment of school shooters.  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 Not Public School Students and Public School Students who find school shooters should be executed.



Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 87 reported that they say no to the question, “should school shooters be executed?” That is, the majority, 58% of the students sampled expressed that school shooters should not be executed.  These sample results will be used to test the claim that the majority of the population of Flagler College students believe that school shooters should not be executed social at a level of significance of 0.05 A pie chart of the data is given below.

Result 2: Pie Chart Should School Shooters be Executed   [Info]
Right click to copy

Hypothesize

             Null: Fifty percent of all Flagler College students believe that school shooters should not be executed.              

Alternate: More than 50% of all Flagler College students believe that school shooters should not be executed.

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 - No execution

Result 3: One sample proportion summary hypothesis test- No Execution   [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
p871500.580.0408248291.95959180.025

Interpret

Since the p-value (<0.025) 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 school shooters should not be executed.

Confidence Interval #1 – Estimating the Population Proportion

             The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that school shooters should not be executed.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that school shooters should not be executed.  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)(0.58) = 87 > 10 and n*(1 – phat) = (150)(1 – 0.58) = (150)(0.42) = 63 > 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-No executions   [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
p871500.580.0402988830.513714240.64628576

Interpret

We are 90% confident that between 51.4% and 64.6% of all Flagler College students find that school shooters should not be executed. This is certainly the majority of all Flagler College students.


Hypothesis Test #2: A contingency table was created to compare the opinions of the Public School Students and the Not Public School Students regarding whether or not school shooters should be executed. Of the 44 Not public School Students, 21 felt school shooters should not be executed and of the 106 Public School Students, 66 felt school shooters not be executed.  That is, 47.7% (21 students out of 44) of the Not Public School Students felt school shooters should not be executed and 62.3% (66 students out of the 106 students) of the Public School Students felt that school shooters should not be executed. With an approximately 14.6% difference in these percentage, the sample gives some reason to believe that the population of Not Public School Students at Flagler College and the population of Public School Students at Flagler College differ in their opinion that school shooters should be executed.

Result 5: Contingency table for Should School Shooters be Executed vs Type of School   [Info]

Contingency table results:


Rows: Type of School
Columns: Should Shooters be Executed
NoYesTotal
Not Public212344
Public6640106
Total8763150

Chi-Square test:


StatisticDFValueP-value
Chi-square12.69731890.1005


Result #5 (contingency table)

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 Not Public Schooled Students at Flagler College and the proportion of the population of Public Schooled Students at Flagler College who feel school shooters should not be executed.

Alternate: There is a difference in the proportion of the population of Not Public Schooled Students at Flagler College and the proportion of the population of Public Schooled Students at Flagler College who feel school shooters should not be executed.

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) = (21 + 66)/(44 + 106) = 87/150 = 0.58

Sample One (Not Public School Students): Since n1*p-hat = (44)(0.58) = 25.52 > 10 and

n1*(1 - p-hat) = (44)(1 – 0.58) = (44)(0.42) = 18.48 > 10, sample one is large.

Sample Two (Public Schooled Students): Since n2*p-hat = (106)(0.58) = 61.48 > 10 and

n2*(1 - p-hat) = (106)(1 – 0.58) = (106)(0.42) = 44.52> 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 Public Schooled Students and the Not Public Schooled.

Result 6: Two sample proportion summary hypothesis test Should School Shooters be Executed   [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 - p2214466106-0.145368780.08851258-1.64235170.1005

Interpret

Since the p – value = 0.1005 is greater than the level of significance of 0.05, the null hypothesis will not be rejected.  Therefore, there is not sufficient evidence that a difference exists in the proportion of the population of Not Public Schooled Students at Flagler College and the proportion of the population of Public Schooled Students at Flagler College who feel school shooters should not be executed.

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

The hypothesis test gave us sufficient evidence that there is not a significant difference in the opinion that the belief of whether or not school shooters should be executed between the population of Not Public Schooled  Students at Flagler College and the population of Public Schooled Students at Flagler College Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions can 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 = (44)(0.477) = 20.988 > 10 and

n1*(1 - p-hat1) = (44)(1 – 0.477) = (44)(0.523) = 23.012 > 10, sample one is large.

Sample Two (Unsocial Students): Since n2*p-hat2 = (106)(0.623) = 66.038 > 10 and

n2*(1 - p-hat2) = (106)(1 – 0.623) = (106)(0.377) = 39.962 > 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 that went to public school, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are Not Public Schooled Students and (0.50)(2500) = 1250 students who are Public Schooled Students in the population.

Population One (Not Public Schooled Students): Since 10n1 = (10)(44) = 440 < 1250, population one is big.

Population Two (Public Students): Since 10n2 = (10)(106) = 1060 < 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: Should School Shooters be Exeuted 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 - p2214466106-0.145368780.088806947-0.31942720.028689635

Result 7: Two sample proportion summary confidence interval - Not Public Schooled Students Vs. Should School Shooters be Executed   

Interpret

 

This confidence interval is negative to positive and covers through 0; this indicates that the percentage of the population of all Not Public Schooled Students who feel school shooters should not be executed is equal to the percentage of the population of all Public Students who feel school shooters should not be executed.  Thus, we are 95% confident that there could be no significant difference in the percent of Not Public schooled and Public Schooled students who believe that school shooters should be executed.


Conclusion

In this report, the sample provided evidence that the majority of all Flagler College students believe school shooters should not be executed. In fact, it was estimated that between 51.4% and 64.6% of all Flagler College students find that school shooters should not be executed. Furthermore, it was found that there is statistical evidence that those students who went to public school were more likely to think school shooters should not be executed versus the students who did not attend a public school.  It was estimated thatthere could be no significant difference in the percent of Not Public schooled and Public Schooled students who believe that school shooters should not be executed.  I would assume school is a place where students should not have to worry about their safety, and students would want serious consequences to someone who is a threat to their safety and friends at school.  Hence, it is interesting that the majority of students at Flagler College feel school shooters should not be executed. Maybe a punishment of life in prison with constant reminder of what school shooters did is a more justable punishment in some people's minds.  It may be more of a punishment than just dying and not have to live with the consequences the rest of one's life. Although, some people’s reaction to someone killing another person would be to have the other person killed, it is clear that majority of Flagler College Students do not believe in executing school shooters.  On the other hand, Flagler College Students could believe that spending the rest of one's life in prison is a much more cruel punishment than killing someone for harming/killing others. Times are always changing, and the amount of violence in school has been increasing, hopefully one day there will be a punishment for school shooters that will make them think twice about what their harmful actions due to the consequences.



Data set 1. Curry, Lee, and McDonal - Flagler College Students   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=87039">Phase 3: School Shootings</A>

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