Introduction:
On the first phase of this project, the views on the military were taken from a sample of 150 Flagler College students from Fall 2017 and Spring 2018 semesters were explored. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as ProFunding and NonFunding. The term “ProFunding” defined the sample of those Flagler College students who think that the U.S Government should continue spending on armed forces and the term “NonFunding” defined the sample of Flagler College students who do not think the U.S Government should spend less on armed forces. There are 47 ProFunding Students and 103 NonFunding Students.
On this phase of the report, attention will be given to students’ opinions on whether or not they think the U.S.
Government should spent less money on armed forces or not.
First, methods of statistical inference will be used to determine if the sample results indicate that a majority of the population of all Flagler College Students think that the government should continue to fund to armed forces. A hypothesis test will first be run to find statistical evidence of majority and then a conference interval will be created to estimate the percentage of the population of Flagler College Students who feel that the Government should continue spending on armed forces.
Second, the sample results will also be used to determine if the population of all ProFunding and the population of all NonFunding students at Flagler College will have a statistically significant difference of opinion regarding if they anyone should be able to serve reagrdless of their sexual preference. 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 percentage of ProFunding and NonFunding students who think all ablebodied citizens should have to serve one year in the military.
Hypothesis Test #1 A Claim of Majority
In a sample of 150 students, 103 reported that the government should spend less on armed forces and more on education and the environment. That is, the majority, 68.67%, of the students sampled expressed that the government should spend less on armed forces. These sample results will be used to test the claim that the majority of Flagler College students think that the government should spend less on armed forces at a level of significance of 0.05. A pie chart of the data if given below.
Hypothesize
Null: Fifty percent of all Flagler College students believe that the government should spend less on armed forces.
Alternate: More than 50% of all Flagler College students believe that the government should spend less on armed forces.
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 np_{0} = (150) (0.50) = 75 > 10 and n(1p_{0}) = (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
One sample proportion summary hypothesis test:
p : Proportion of successes H_{0} : p = 0.5 H_{A} : p > 0.5 Hypothesis test results:

Interpret
Since the pvalue (
Confidence Interval #1 Estimating the Population Proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College student feel that the government should spend less on armed forces. Therefore, a confidence interval will be created to estimate the percent of Flagler College students who believe that the government should spend less on armed forces. 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)(0.6867) = 103 > 10 and n*(1 – phat) = (150)(1– 0.6867) = (150)(0.3133) = 47 > 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 90% confidence interval results:

Interpret
We are 90% confident that between 62.4% and 74.9% of all Flagler College Students find that the government should spend less on armed forces. This is certainly a majority of all Flagler College Students.
Hypothesis Test #2 A Claim of differences between two Population Proportions
A contingency table was created to compare the opinions of the ProFunding Students and NonFunding Students regarding the opinion of joining the military regardless of their sexual preference. Of the 103 NonFunding Students 101 of them thought anyone should be able to join regardless of their sexual preference and of the 47 ProFunding Students, 42 of them think anyone should be able to join regardless of their sexual preference. That is 98.1% (101 students out of 103 students) of the NonFunding students think that it is okay to join the military regardless of sexual preference and 89.4% of ProFunding thought that it was okay to join the military regardless of sexual preference. With an approximately 9% difference in these percentages, the sample gives some reason to believe that the population of ProFunding students and the population of NonFunding students slightly differ in their opinion that the government should spend less on armed forces.
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.
Contingency table results:
Rows: Do you think that the U.S. government should spend less money on our armed forces and more on education and the environment? Columns: Do you think that persons should be allowed to join and serve in the military regardless of their sexual preference as long as their behavior meets strict military standards?
ChiSquare test:
ChiSquare suspect. 
Prepare:
1. Large Samples – It is found that the pooled sample proportion is
phat = (x_{1} + x_{2})/ (n_{1} + n_{2}) = (101 +42)/(103 + 47) = 143/150 = 0.9533
Sample One (Social Students): Since n_{1}*phat = (103) (0.9533) = 98.2 > 10 and
n_{1}*(1  phat) = (103) (1 – 0.9533) = (103) (0.0467) = 4.8 < 10, sample one is not large.
Sample Two (Unsocial Students): Since n_{2}*phat = (47) (0.9533) = 44.8 > 10 and
n_{2}*(1  phat) = (47) (1 – 0.9533) = (47)(0.0467) = 2.2 <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 Social Students and the Unsocial Students.
Compute
Two sample proportion summary hypothesis test:
p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions H_{0} : p_{1}  p_{2} = 0 H_{A} : p_{1}  p_{2} ≠ 0 Hypothesis test results:

Interpret
Since the pvalue= 0.0192 is less than the level of significance of 0.05, the null hypothesis will be rejected. Therefore, there is sufficient evidence that there exists a difference in the proportion of ProFunding students at Flagler College and the proportion of NonFunding Students at Flagler college who feel the government should spend less on armed forces.
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 the government should spend less money on armed forces between the population of ProFunding Students at Flagler College and the population of NonFunding Students at Flagler College. Therefore, a confidence interval will be created to estimate the 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 n_{1}*phat_{1} = (103) (.98) = 100.9 > 10 and
n_{1}*(1  phat_{1}) = (103) (1 – .100) = (103) (.900) = 10.3 > 10, sample one is large.
Sample Two (Unsocial Students): Since n_{2}*phat_{2} = (47)(0.89) = 41.83> 10 and
n_{2}*(1  phat_{2}) = 103 (1 – 0.98) = (81)(0.2) = 16.2 > 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 socially by social media, we will assume 50% are and 50% are not. Hence, there are approximately (0.50)(2500) = 1250 students who are Social Students and (0.50)(2500) = 1250 students who are Unsocial Students in the population.
Population One (Social Students): Since 10n_{1} = (10)(103) = 1030 < 1250, population one is big.
Population Two (Unsocial Students): Since 10n_{2} = (10)(47) = 47< 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:
p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions 95% confidence interval results:

Interpret
The confidence interval is completely negative; this indicates that the percentage of the population of all ProFunding students who feel the government should continue to spend on armed forces is less than the population of NonFunding students who think the government should spend less on armed forces. Thus I am 95% confident that the percentage of all NonFunding students who feel the government should spend less is between 5.1% and 17.9%. greater than the percentage of all ProFunding students who think the government should spend less on armed forces.
Conclusion
Society often does not realize the time and effort put in by those who are of the armed forces. In this report, the sample provided evidence that the majority of all Flagler College Students find that the government should spend less on armed forces and more on education and the environment. In fact it was estimated that between 62.4% and 74.9% of all Flagler College Students think the government should spend less on armed forces.
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