PHASE THREE: Traveling Habits of Flagler College Students in Spring 2019
Introduction:
On the first phase of this project, the social media habits of a sample of 150 Flagler College Students from Spring semester 2019 was explored. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as the Optional Students and the Required Students. The term “Optional Students” defined the sample of those Flagler College students who do not think students should be required to study abroad and the term ”Required Students” will refer to the sample of those Flagler College students who do think students should be required to study abroad. There are 70 Optional Students and 80 required Students sampled. A bar chart representing the two samples is presented below.
On this phase of the report, attention will be given to students’ opinions about travel abroad being necessary for teaching broader diversity.
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 traveling abroad is necessary for diversity. 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 travel abroad is necessary for diversity.
Second, the sample results will also be used to determine if the opinion of the population of all Optional Students and the population of all Required Students at Flagler College have a statistically significant difference of opinion regarding the diversity caused by travel abroad. 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 Optional Students and Required Students who find travel abroad to be necessary for diversity.
Hypothesis Test #1 – A Claim of Majority
In the sample of 150 students, 115 reported that travel abroad is necessary for diversity. That is, the majority, 76.67%, of the students sampled expressed that travel abroad is necessary. These sample results will be used to test the claim that the majority of the population of Flagler College students view travel abroad as a necessary choice at a level of significance of 0.05. A pie chart of the data is given below.
Hypothesize
Null: fifty percent of all Flagler College students believe that travel abroad is necessary for diversity.
Alternate: more than 50% of all Flagler College students believe that travel abroad is necessary for diversity.
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 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
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 (<0.0001) 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 travel abroad is necessary for diversity.
Confidence Interval #1 – Estimating the Population Proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that travel abroad is necessary for diversity. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe the travel abroad is necessary for diversity. 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) (0.7667) = 115 > 10 and n*(1  phat) = (150) (1 0.7667) = (150) (0.2333) = 35 > 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 approximately 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 71.0% and 82.3% of all Flagler College students find that travel abroad is necessary for diversity. 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 Optional Students and the Required Students regarding the diversity caused by travel abroad. Of the 70 Optional Students, 55 felt travel abroad was necessary and of the 80 Required Students, 60 felt travel abroad was necessary. That is, 78.6% (55 students out of 70) of the Optional Students felt study abroad was a necessary choice for diversity and 75% (60 students out of the 80) out of the Required Students felt travel abroad was necessary. With an approximately 3.6% difference in these percentages, the sample gives some reason to believe that the population of Optional Students at Flagler College and the population of Required Students at Flagler College don’t differ in their opinion that travel abroad is a necessity for diversity.
Contingency table results:Rows: Required Columns: Diversity
ChiSquare test:

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 Optional Students at Flagler College and the proportion of the population of Required Students at Flagler College who feel travel abroad is necessary.
Alternate: There is a difference in the proportion of the population of Optional Students at Flagler College and the proportion of the population of Required Students at Flagler Collee who feel study abroad is necessary.
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 = (x^{1} + x^{2}) / (n_{1} + n_{2}) = (55 + 60) / (70 + 80) = 115/150 = 0.7667
Sample One (Optional Students): Since n_{1}*phat = (70) (0.7667) = 53.7 > 10 and n_{1}*(1 – phat) = (70) (1 – 0.7667) = (70) (0.2333) = 16.3 > 10, sample one is large.
Sample Two (Required Students): Since n_{2}*phat = (80) (0.7667) = 61.3 > 10 and n_{2}*(1 – phat) = (80) (1 – 0.7667) = (80) (0.2333) = 18.7 > 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 Optional Students and the Required 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 = 0.6059 is greater than the level of significance of 0.05, the null hypothesis will not be rejected. Therefore, there is sufficient evidence that there is no difference in the proportion of the population of Optional Students at Flagler College and the proportion of the population of Required Students at Flagler College who feel study abroad is necessary for diversity.
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 study abroad is necessary for diversity between the population of Optional Students at Flagler College and the population of Required 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 students responses were taken in such a way that their responses were independent of each other
2. Large Samples –
Sample One (Optional Students): Since n_{1}*phat_{1} = (70) (0.786) = 55 > 10 and n_{1}*(1 – phat_{1}) = (70) (1 – 0.786) = (70) (0.214) = 15 > 10, sample one is large.
Sample Two (Required Students): Since n_{2}*phat_{2} = (80) (0.75) = 60 > 10 and n_{2}*(1 – phat_{2}) = (80) (10.75) = (80) (0.25) = 20 > 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 study abroad, we will assume 50% are and 50% are nor. Hence, there are approximately (0.50) (2500) = 2500 students who are Optional Students in the population.
Population One (Optional Students): Since 10n_{1} = (10) (70) = 700 < 1250, population one is big.
Population Two (Required Students): Since 10n_{2} = (10) (80) = 800 < 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
This confidence interval contains zero; this indicates that the percentage of the population of all Required Students who feel study abroad is necessary for diversity is equal to the percentage of the population of all Required Students who feel study abroad is necessary for diversity. Thus, I am 95% confident that the percentage of all Required Students who feel study abroad causes greater diversity is equal to the percentage of all Optional Students who feel study abroad is necessary.
Conclusion
Society has embraced the idea of earning a degree and the diversity of our education is an important topic. In this report, the sample provided evidence that the majority of all Flagler College students find study abroad necessary for greater diversity. In fact, it was estimated that between 71.0% and 82.3% of all Flagler College students find that travel abroad is necessary for diversity. Furthermore, it was found that there is statistical evidence that there is no difference of opinion between Optional Students and Required Students about study abroad being necessary for diversity. It was estimated that a zero is contained in the interval of Flagler College students who feel study abroad is necessary than all other Flagler College students. This is natural association to me. I feel study abroad can help improve my understanding of a culture by being subjected firsthand to the environment and people. I now know I am not alone.
The underlying purpose of study abroad is to help broaden experiences and culturalawareness. Hence, it is not a surprise that the majority of students feel study abroad is necessary for greater diversity. Maybe a policy of taking one semester or quarter abroad would encourage students to become more culturally diverse and see the world outside the U.S. Although enforcing such a policy would be difficult, it is something to consider. On the other hand, it is financially costly to send one person across the world for their education, and some may not have the money to do so. Times are always changing, but humans are curious animals so hopefully a balance between abroad and native culture will be met with the next generations.
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