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PHASE THREE: Views On The Military Of Flagler College Students Fall 2017 and Spring 2018
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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 Pro-Funding and Non-Funding.  The term “Pro-Funding” defined the sample of those Flagler College students who think that the U.S Government should continue spending on armed forces and the term “Non-Funding” defined the sample of Flagler College students who do not think the U.S Government should spend less on armed forces. There are 47 Pro-Funding Students and 103 Non-Funding 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 Pro-Funding and the population of all Non-Funding 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 Pro-Funding and Non-Funding students who think all able-bodied 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.

Result 1: Result 1:Pie Chart with Data- Military Spending- Less or More   [Info]
Right click to copy

 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 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 2: One sample proportion summary hypothesis test- Spending   [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
p1031500.686666670.0408248294.5723809<0.0001

 

Interpret

 

 

Since the p-value (

 

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

 

Result 3: One sample proportion summary confidence interval- Spending   [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
p1031500.686666670.0378730820.624370990.74896234

 

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 Pro-Funding Students and Non-Funding Students regarding the opinion of joining the military regardless of their sexual preference. Of the 103 Non-Funding Students 101 of them thought anyone should be able to join regardless of their sexual preference and of the 47 Pro-Funding 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 Non-Funding students think that it is okay to join the military regardless of sexual preference and 89.4% of Pro-Funding 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 Pro-Funding students and the population of Non-Funding 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.

 

Result 4: Contingency table (with data)-Sexual Preference   [Info]
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?
NoYesTotal
No54247
Yes2101103
Total7143150

Chi-Square test:
StatisticDFValueP-value
Chi-square15.48638510.0192
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Prepare:

1.       Large Samples – It is found that the pooled sample proportion is

 

p-hat = (x1 + x2)/ (n1 + n2) = (101 +42)/(103 + 47) = 143/150 = 0.9533

Sample One (Social Students): Since n1*p-hat = (103) (0.9533) = 98.2 > 10 and

n1*(1 - p-hat) = (103) (1 – 0.9533) = (103) (0.0467) = 4.8 < 10, sample one is not large.

Sample Two (Unsocial Students): Since n2*p-hat = (47) (0.9533) = 44.8 > 10 and

n2*(1 - p-hat) = (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

Result 5: Two sample proportion summary hypothesis test- Table   [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 - p24247101103-0.0869655030.037128198-2.34230340.0192

Interpret

Since the p-value= 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 Pro-Funding students at Flagler College and the proportion of Non-Funding 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 Pro-Funding Students at Flagler College and the population of Non-Funding 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 n1*p-hat1 = (103) (.98) = 100.9 > 10 and

n1*(1 - p-hat1) = (103) (1 – .100) = (103) (.900) = 10.3 > 10, sample one is large.

Sample Two (Unsocial Students): Since n2*p-hat2 = (47)(0.89) = 41.83> 10 and

n2*(1 - p-hat2) = 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 10n1 = (10)(103) = 1030 < 1250, population one is big. 

Population Two (Unsocial Students): Since 10n2 = (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

Result 6: Two sample proportion summary confidence interval- Non-Funding   [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 - p24247101103-0.0869655030.046984378-0.179053190.0051221865

Interpret

The confidence interval is completely negative; this indicates that the percentage of the population of all Pro-Funding students who feel the government should continue to spend on armed forces is less than the population of Non-Funding students who think the government should spend less on armed forces. Thus I am 95% confident that the percentage of all Non-Funding students who feel the government should spend less is between 5.1% and 17.9%. greater than the percentage of all Pro-Funding 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.

 

 

 

 


 

 

 

 

 

HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=78302">PHASE THREE: Views On The Military Of Flagler College Students Fall 2017 and Spring 2018</A>

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