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Phase Three: Travelling Preferences of Flagler College Statastics 223 Students in Fall 2018

Phase Three

Introduction

On the first phase of this project, the travel of a sample of 150 Flagler College students from fall 2018 was explored. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as “J-Mester” and “May-Mester.” The term “J-Mester” defined the sample of those Flagler College students who would prefer to study during the month of January and the term “May-Mester” defined the sample of those Flagler College students who prefer to study during the month of May. There are 69 J-Mester students and 81 May-Mester students sampled. A bar chart representing the two samples is presented below.

Result 1: J-Mester vs. May-Mester Bar Plot   [Info]

On this phase of the report, attention will be given to students’ opinions about whether or not traveling provides a real-life education.

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 believe that if travel does provide a real-lifeexperience. A hypothesis test will be ran 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 believe travel does provide a real life education.

Second, the sample results will also be used to determine if the opinion of the population of all J-Mester students and the population of all May-Mester students at Flagler College will have a statistically significant difference of opinion regarding whether or not travel provides a real-life education. Again, a hypothesis test will be ran 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 J-Mester students and May-Mester students who find that travel provides a real life education.

Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 146 reported that traveling does provide a real-life education. That is, the majority, 97.33%, of the students sampled expressed that traveling does provide a real-life education. These sample results will be used to test the claim that the majority of the population of Flagler College students view traveling as a provider of real-life education at a level of significance of 0.05. A pie chart of the data is given below.

Result 2: Real Life Education   [Info]

Hypothesize

Null: Fifty percent of all Flagler College students believe that travel does provide a real-life education

Alternate: More than fifty percent of all Flagler College students believe that travel does provide a real-life education

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.

1. Large Sample - Since np0 = (150)(.50) = 75 ≥ 10 and n(1-p0 ) = (150)(.50) = 75 ≥ 10 are both true statements, the sample is large.

1. Big Population – Since 10n = (10)(150) = 1500 < 2500, the population is big, recall Flagler College has a population of approximately 2500 students.

1. Independence within Sample – Yes, the student responses were taken in such a way that their responses were independent of one another.

Compute

Result 3: Test of Majority   [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
p1461500.973333330.04082482911.594251<0.0001

Interpret

Since the p-value (<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 traveling does provide a real-life education.

Confidence Interval #1 – Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that traveling does provide a real-life education. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that traveling does provide a real-life education. Since a one-tailed test with a level of significance of 0.05 was ran, 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)(0.9733) = 146 > 10 and n*(1 – phat) = (150)(1 – 0.9733) = (150)(0.0267) = 4 < 10, the sample is small.

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

Compute

Result 4: Confidence Interval   [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
p1461500.973333330.0131543540.951696350.99497032

Interpret

We are 90% confident that between 95.17% and 99.50% of all Flagler College students find that travel provides a real life education. This is certainly the majority of all Flagler College students.

Hypothesis Test #2- A Claim of the Difference between two Population Proportions

This contingency table compares the opinions of students who prefer studying during a J-Mester and students who prefer studying during a May-Mester in regards to whether they believe traveling gives students a real-life education.  Out of the students who prefer J-Mester studying, 65 of the 69 believe travelling provides a real-life education. This concludes that 94.2% of J-Mester students believe travelling is essential to real-life education. All of the students who prefer May-Mester studying believe travelling provides students with a real-life education. This is 100% of the May-Mester students. With about a 6% difference in these percentages, the sample gives reason to believe that the vast majority of J-Mester and May-Mester liking students believe a real-life education can be gained through travelling.

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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 ran at a level of significance at 0.05.

Hypothesize

Null – There is no difference in the proportion of the population of J-Mester students at Flagler College and the proportion of the population of May-Mester students at Flagler College who believe that travel provides a real-life education.

Alternate – There is a difference in the proportion of the population of J-Mester students at Flagler College and the proportion of the population of May-Mester students at Flagler College who believe that travel provides a real-life education.

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) = (65+ 81)/(81 + 69) = 146/150 = 0.9733

Sample One (J-Mester): Since n2*p-hat = (69)(0.9733) = 67.2 > 10 and

n2*(1 - p-hat) = (69)(1 – 0.9733) = (69)(0.0267) = 1.8 < 10, sample one is small.

Sample Two (May-Mester): Since n1*p-hat = (81)(0.9733) = 78.8 > 10 and

n1*(1 - p-hat) = (81)(1 – 0.9733) = (81)(0.0267) = 2.2 < 10, sample two is small.

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 J-Mester and the May-Mester.

Compute

Result 6: Hypothesis Test 2   [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 - p265698181-0.0579710140.026393303-2.1964290.0281

Interpret

Since the p – value = .0281 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 the population of J-Mester students at Flagler College and the proportion of the population of May-Mester students at Flagler College who feel travel does provide a real-life education.

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 travel does provide a real-life education between the population of J-Mester students at Flagler College and the population of May-Mester students 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 ran, a 95% confidence interval will be created.

Prepare

1. Random Samples with Independent Observations- It is safe to assume that the samples compared are random. It is not known for certain, but to continue to analyze the data we will assume they are independent of one another.

1. Large Samples-
Sample One (J-Mester Preference): Since n1*p-hat1 = (65)(.940) = 61.1 ≥ 10

Page Break

Sample Two (May-Mester Preference): Since n2*p-hat1 = (69)(1) = 69 ≥ 10

1. Big Populations- With Flagler College having a study body of 2,500 students, that of which only Statistic 223 Students in Fall 2018 were surveyed, we must assume 50% have a preference of when to study and 50% do not. This being said, there are approximately (.50)(2500) = 1250 students who have a preference of when to study and (.50)(2500) = 1250 students who do not have a preference.
Population One (J-Mester): Since 10n1 = (10)(65) = 6500 sample one is big.
Population Two (May-Mester): Since 10n2 = (10)(69) = 6900 sample two is big.

1. Independent Samples- The samples were collected to determine that they were independent of each other

Compute

Result 7: Confidence Interval 2   [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 - p265698181-0.0579710140.028132805-0.1131103-0.0028317297

Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all J-Mester students who feel traveling provides a real-life experience is less than the percentage of the population of all May-Mester Students who feel traveling provides a real-life experience.  Thus, I am 95% confident that the percentage of all May-Mester Students who feel traveling provides a real-life experience is between .28% and 11.3% greater than the percentage of all J-Mester Students who feel traveling provides a real-life experience.

Conclusion

In this report, the sample provided evidence that the majority of all Flagler College students find that traveling provides a real-life education. In fact, it was estimated that 95.17% and 99.50% of all Flagler College students find that travel provides a real-life education.  Furthermore, it was found that there is statistical evidence that J-Mester students who feel traveling provides a real-life experience is less than the percentage of May-Mester students who feel traveling provides a real-life experience.  It was estimated that between .28% and 11.3% of all Flagler College students that feel traveling provides a real-life experience prefer to study during the May-Mester.

During Hypothesis Test 1, the result of the Big Population and Large Sample tests the sample size was small in comparison to the total large population. This is because only Statistic 223 students of Flagler College answered the survey. We are unable to survey the entire population, thus not meeting all the requirements of the Central Limit Theorem. However, we persisted to complete this report.

Result 5: Contingency table Real Life   [Info]
Contingency table results:
Rows: J-mester or May-mester
Columns: Real Life Education
 No Yes Total J-mester 4 65 69 May-mester 0 81 81 Total 4 146 150

Chi-Square test:
StatisticDFValueP-value
Chi-square14.82430020.0281
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.