Print - Back

Phase Three: School Shootings with Brianna, Zach and Elena
Generated Dec 11, 2018 by elewis039

In the first phase of the project 150 Flagler College students were surveyed about their positions on school shootings. In the second phase of the project the same sample of students was divided into two smaller groups which were described as "agree" and "disagree". The term "agree" describes the students who agree with execution of school shooters, while the term "disagree" refers to students who do not agree with the execution of school shooters. There are 65 students who agree with execution and 85 students who do not agree with execution. A bar chart representing the two samples is below.

embed<result1>

On this phase of the report, attention will be given to the student's opinions about the Government not doing enough to protect children.

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 the Government is not doing enough to protect children. 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 the Government is not doing enough to protect children.

Second, the sample results will also be used to determine if the opinion of the population of all students who agree with execution and the population of all students who disagree with execution have a statistically significant difference of opinion regarding the Government not doing enough to protect children. Another 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 Agree students and Disagree students who find the Government is not doing enough to protect children.

Hypothesis Test #1- A claim of majority

In the sample of 150 students, 130 reported that they feel the Government is not doing enough to protect children. That is, the majority, 86.67%, of the students sampled expressed that the Government is not doing enough to protect children. These sample results will be used to test the claim that the majority of all Flagler College students believe the Government is not doing enough to protect children at a level of significance of 0.05. A pie chart of data is given below.

embed<result2>

Hypothesize

Null: Fifty percent of all Flagler College students believe that the Government is not doing enough to protect children.

Alternate: More than fifty percent of all Flagler College students believe the Government is not doing enough to protect children.

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

Prepare

1. Random sample- Probably not, (but we hope it is representative) and 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 approximately 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

embed<result3>

Interpret

Since the p-value (sufficient evidence to support the claim that the majority of all Flagler College students feel that the Government is not doing enough to protect children.

Confidence Interval 1- Estimating the population proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students believe the Government is not doing enough to protect children. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe the Government is not doing enough to protect children. Since a one tailed test with a significance level 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's responses were taken in such a way that their responses were independent of each other.

2. Large Sample- Since n*phat = (150) (0.8667) = 130 > 10 and n*(1- phat) = (150)(1-0.8667) = (150)(0.1333) = 20 > 10, the sample is large.

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

Compute

embed<result4>

Interpret

We are 90% confident that between 82.1% and 91.2% of all Flagler College students find that the Government is not doing enough to protect children. This is certainly the majority of all Flagler College students.

Hypothesis Test #2- A claim of difference between two population proportions

A contingency table was created to compare the opinions of Agree students and Disagree students regarding if the Government is doing enough to protect children, pertaining to school shootings.  Of the 85 students who do not believe in execution 75 believed the Government is not doing enough. Of the 65 students who agree with execution of a school shooter, 55 feel the Government is not doing enough to protect children. That is, 88.2% (75 out of 85) of students who do not agree with execution felt the Government is not doing enough to protect children and 84.6% (55 out of 65) of students who agree with execution feel that the Government is not doing enough to protect children. With a slight 4% difference in these two percentages, the sample gives no reason to believe that the population of students who agree with execution at Flagler College and the students who do not agree with execution at Flagler College differ in opinion on if the Government is doing enough to protect children.

embed<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 Agree students at Flagler College and the proportion of the population of Disagree Students at Flagler College who feel the government is not doing enough to protect children.

Alternate: There is a difference in the proportion of the population of Agree Students at Flagler College and the proportion of the population of Disagree Students at Flagler College who feel the Government is not doing enough to protect children.

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) = (75 + 55)/ (85 + 65) = 130/150 = 0.8667

Sample One (Disagree Students): Since n1*p-hat = (85) (0.8667) = 73.7 > 10 and

n1*(1 - p-hat) = (85) (1 – 0.8667) = (85) (0.1333) = 11.3 > 10, sample one is large.

Sample Two (Agree Students): Since n2*p-hat = (65) (0.8667) = 56.3 > 10 and

n2*(1 - p-hat) = (65) (1 – 0.8667) = (65) (0.1333) = 8.7 < (less than or equal too) 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 Agree Students and the Disagree Students.

Compute

embed<result6>

Interpret

Since the p-value= 0.5181 is greater than the significance of 0.05, the null hypothesis will not be rejected. Therefore, there is sufficient evidence that there does not exist a difference in the proportion of the population of agree students at Flagler College and the proportion of the population of disagree students at Flagler College who feel the government is not doing enough to protect the government.

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

1. Random Samples with Independent Observations – 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 (Disagree Students): Since n1*p-hat1 = (85) (0.882) = 75  > 10 and

n1*(1 - p-hat1) = (85) (1 – 0.882) = (85) (0.118) > 10, sample one is not large.

Sample Two (Agree Students): Since n2*p-hat2 = (65) (0.846) = 55  > 10 andn2*(1 - p-hat2) = (65)(1 – 0.846) = (65)(0.154)   > 10, sample two is not large.

3. Big Populations – Recall, Flagler College has a population around 2500 students.  Since we are unsure what overall percentage of the students that agree or disagree with execution, we will assume 50% do and 50% do not.  Hence, there are approximately (0.50) (2500) = 1250 students who are Agree Students and (0.50)(2500) = 1250 students who are Disagree Students in the population.

Population One (Disagree Students): Since 10n1 = (10) (85) = 850 < 1250, population one is big.

Population Two (Agree Students): Since 10n2 = (10) (65) = 650 < 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

embed<result7>

Interpret

This confidence interval contains zero; this indicates that the percentage of the population of disagree students who believe the Government is not doing enough to protect children may be equal to the percentage of the population of agree students who believe the Government is not doing enough to protect children. Therefore, because the confidence interval is between -0.0750 and 0.1474, we are 95% confident that there is no statistical difference between disagree and agree students who feel the Government is not doing enough to protect children.

Conclusion

School shootings have had a negative but huge impact on the world. In this report that sample provided evidence that between 82.1% & 91.2% of all Flagler College students believe the Government is not doing enough to protect children from school shootings. Furthermore, it was found that there is not a statistical difference between the students who Disagree with execution and the students who Agree with execution that the Government is not doing enough to protect children. It was found that there is not a statistical difference, and it might be equal, that all Flagler College students feel the Government needs to do more to protect children. School shootings are a horrible occurrence and demand the Governments actions so these tests do not surprise.

Result 1: Result 1: Agree and disagree students sampled   [Info]

Result 2: Result 2: Pie Chart With Data - Is the government doing enough.   [Info]

Result 3: Result 3: One sample proportion summary hypothesis test - Government doing enough.   [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
p1301500.866666670.0408248298.9814624<0.0001

Result 4: Result 4: One sample proportion summary confidence interval- Is the Government doing enough.   [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
p1301500.866666670.0277555470.821012860.91232048

Result 5: Result 5: Contingency table (with data) - Executed vs Is the Gov doing enough   [Info]

### Contingency table results:

Rows: Executed
Columns: Protecting Children
NoYesTotal
No751085
Yes551065
Total13020150

### Chi-Square test:

StatisticDFValueP-value
Chi-square10.417681870.5181

Result 6: Result 6: Two sample proportion summary hypothesis test - Executed vs Is the Gov. doing enough   [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 - p2758555650.0361990950.0560112030.646283120.5181

Result 7: Result 7: Two sample proportion summary confidence interval -executed vs is the gov. doing enough   [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 - p2758555650.0361990950.056780109-0.0750878730.14748606