Phase Three
Introduction:
In the first phase of this study, 150 Flagler College students were surveyed and answered questions about school shootings. For the purpose of this phase of the project, the 150 students will be split into two smaller samples. The students will be split into those who are for concealed carry on campus, and those who are not. For the purpose of this report, the two samples can be defined quite simply. “Pro Concealed Carry on Campus” describes those students who believe that concealed carry should include campuses, and “Against Concealed Carry on Campus” refers to the students who do not believe that concealed carry should extend to campuses. There are 124 Pro Concealed Carry on Campus students and 26 Against Concealed Carry on Campus students in the sample.
Result 1: Opinion on concealed weapons on campuses
On this phase of the report, attention will be given to students’ opinions about whether or not they believe that school shooters should be executed. .
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 think that school shooters should be executed.
Second, the sample results will also be used to determine if the opinion of the population of all concealed carry Students and the population of all Against Concealed Carry on Campus Students at Flagler College have a statistically significant difference of opinion regarding the question if school shooters should be executed. 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 population of Pro Concealed Carry on Campus students and Against Concealed Carry on Campus students who believe that school shooters should be executed.
Hypothesis Test #1 – A Claim of Majority
In the sample of 150 students, 85 reported that they believe that school shooters should not be executed. That is, the majority, 56.67%, of the students sampled expressed the belief 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 feel like school shooters should not be executed at a level of significance of 0.05 A pie chart of the data is given below.
Result 2: Pie Chart With Data  Should School Shooters be Executed?
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 rightsided 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(1p0) = (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  Execution
One sample proportion summary hypothesis test:
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5
Hypothesis test results:
Proportion 
Count 
Total 
Sample Prop. 
Std. Err. 
ZStat 
Pvalue 
p 
85 
150 
0.56666667 
0.040824829 
1.6329932 
0.0512 
Interpret
Since the pvalue (.0512) is larger than the level of significance of 0.05, the null hypothesis cannot be rejected. Therefore, there is not enough 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 95% 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)(0.5667) = 85 > 10 and n*(1 – phat) = (150)(1 – 0.5667) = (150)(0.4333) = 65 > 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
One sample proportion summary confidence interval:
p : Proportion of successes
Method: StandardWald
95% confidence interval results:
Proportion 
Count 
Total 
Sample Prop. 
Std. Err. 
L. Limit 
U. Limit 
p 
85 
150 
0.56666667 
0.040460314 
0.48736591 
0.64596743 
Interpret
We are 95% confident that between 48.7% 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 Claim of the Difference between two Population Proportions
A contingency table was created to compare the opinions of the Pro Concealed Carry on Campus Students and the Against Concealed Carry on Campus Students regarding whether or not school shooters should be executed. Of the 26 Pro Concealed Carry on Campus Students, 10 felt school shooters should not be executed and of the 124 Against Concealed Carry on Campus Students, 75 felt that school shooters should not be executed. That is, 38.5% (10 students out of 26) of the Pro Concealed Carry on Campus Students felt that school shooters should not be executed and 60.5% (75 students out of the 124 students) of the Against Concealed Carry on Campus Students felt that school shooters should not be executed. With an approximately 22% difference in these percentage, the sample gives some reason to believe that the population of Pro Concealed Carry on Campus Students at Flagler College and the population of Against Concealed Carry on Campus Students at Flagler College differ in their opinion on whether or not school shooters should be executed.
Result 5: Contingency table (with data)  Against Concealed Carry Vs. Execution
Contingency table results:
Rows: Sample(Concealed Weapons)
Columns: Sample(Executed)
No 
Yes 
Total 

No 
75 
49 
124 
Yes 
10 
16 
26 
Total 
85 
65 
150 
ChiSquare test:
Statistic 
DF 
Value 
Pvalue 
Chisquare 
1 
4.2450288 
0.0394 
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 Pro concealed carry students at Flagler College and the proportion of the population of students against concealed carry at Flagler College who feel like school shooters should not be executed.
Alternate: There is a difference in the proportion of the population of pro concealed carry students at Flagler College and the proportion of the population of students against concealed carry at Flagler College who feel like 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
phat = (x1 + x2)/(n1 + n2) = (85)/(26 + 124) = 85/150 = 0.5667
Sample One (Pro Concealed Carry): Since n1*phat = (26)(0.5667) = 14.7 > 10 and
n1*(1  phat) = (26)(1 – 0.7133) = (26)(0.4333) = 11.3 > 10, sample one is large.
Sample Two (Against Concealed Carry): Since n2*phat = (124)(0.5667) = 70.3 > 10 and
n2*(1  phat) = (124)(1 – 0.5667) = (124)(0.4333) = 53.7 > 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 pro concealed carry students and the anti concealed carry students.
Compute
Result 6: Two sample proportion summary hypothesis test  Against Concealed Carry Vs. Execution
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:
Difference 
Count1 
Total1 
Count2 
Total2 
Sample Diff. 
Std. Err. 
ZStat 
Pvalue 
p1  p2 
15 
26 
70 
124 
0.012406948 
0.10688653 
0.11607587 
0.9076 
Interpret
Since the p – value = 0.9076 is more than the level of significance of 0.05, the null hypothesis will not be rejected. Therefore, there is not sufficient evidence that there exists a difference in the proportion of the population of pro concealed weapons students at Flagler College and the proportion of the population of students against concealed carry 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 a significant difference in the opinion that school shooters should not be executed between the population of pro concealed carry students at Flagler College and the population of students against concealed carry 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 (Pro Concealed Carry): Since n1*phat1 = (26)(0.577) = 15 > 10 and
n1*(1  phat1) = (26)(1 – 0.577) = (26)(0.423) = 11 > 10, sample one is large.
Sample Two (Against Concealed Carry): Since n2*phat2 = (124)(0.562) = 70 > 10 and
n2*(1  phat2) = (124)(1 – 0.562) = (124)(0.38) = 47 > 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 are or are not affected by concealed carry, we will assume 50% are and 50% are not. Hence, there are approximately (0.50)(2500) = 1250 students who are pro concealed carry and (0.50)(2500) = 1250 students who are against concealed carry in the population.
Population One (pro concealed carry): Since 10n1 = (10)(26) = 260 < 1250, population one is big.
Population Two (against concealed carry): Since 10n2 = (10)(124) = 1240 < 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 
15 
26 
70 
124 
0.012406948 
0.10663191 
0.19658775 
0.22140164 
Interpret
This confidence interval is partially negative; this indicates that the percentage of the population of all Pro Concealed Carry on Campus Students who feel that school shooter should not be executed is less than the percentage of the population of all Against Concealed Carry on Campus Students who feel that school shooters should not be executed. Thus, I am 95% confident that the percentage of all Against Concealed Carry on Campus Students who feel that school shooters should not be executed is between 19.6% and 22.1% greater than the percentage of all Against Concealed Carry on Campus Students who feel that school shooters should not be executed.
Conclusion
The debate between concealed carry on campus and execution has being an increasingly popular topic of debate. In this report, the sample provided evidence that the majority of all Flagler College students find that school shooters should not be executed. In fact, it was estimated that between 48.7% 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 are Against Concealed Carry on Campus are more likely to believe that school shooters should not be executed. It was estimated that between 19.6% and 22.1% more of all Flagler College students with opinions against concealed carry were more likely to be against executing school shooters than all other Flagler College students.
With the increase in the amount of school shootings across the United States, it is becoming more important to increase awareness around this topic and to get the opinions of students across the country. More studies like this one will help to start the conversation about these tough topics and help to construct solutions to this problem.
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