PHASE THREE: More/Less Likely to Divorce Among Flagler College Students in Spring 2019
Introduction:
During the first phase of this project, the status of parental marriage on a sample of 150 Flagler College Students from the Spring Semester of 2019 was surveyed. Throughout the second phase, the sample of Flagler students was explored into two smaller sub groups. The term “More Likely” defines the students who are more persuaded to divorce based on their parent’s marital status. The term “Less Likely” categorizes the students who are less persuaded to get a divorce based on their parent’s marriage. There are 56 More Likely and 94 Less Likely sampled. A bar chart representing the two samples is presented below.
Result 1: More Likely and Less Likely
In this phase of the report, we will give our attention to those students who are more or less likely to get divorced based on their parent’s marital status.
First, statistical data will be used to interpret if the sample size of students to indicate if the majority of Flagler College Students’ are more or less likely to get divorced. We will first run a hypothesis test to identify the majority and then the confidence interval will be created to identify the percentage of Flagler College Students who are more or less likely to get a divorce.
Second, the sample identified will be used to determine if the opinion of the population of all more likely students and the population of all less likely students have a significant statistical difference regarding to if their parents are married or divorced. Once again, we will apply the data given to run another hypothesis test to gather statistical evidence of a difference and then a confidence interval will be run to determine the difference to identify the percentage of students who are more or less likely to get divorced. Then we’ll make a decision based on their parent’s marital status.
Hypothesis Test #1 – A Claim of Majority
Among the 150 Flagler College Students sampled, 94 reported that they are less likely to divorce based on their parent’s marital status. We can safely identify Students that are “less likely” as the majority, which is represented as 62.67% of the sample. With the sample data collected we can use this data to test the claim that those whose parents are divorced are more likely to divorce; using a significance level of 0.05. Below is a pie chart to represent the data.
Result 2: Pie Chart with Data – More or Less Likely to Divorce
Hypothesize
Null: Fifty percent of all Flagler College students are less likely to divorce.
Alternate: More than 50% of all Flagler College are less likely to divorce.
Based on the alternate hypothesis, this is a right onesided test.
Prepare
0. Random Sample – We assume that this sample of 150 Flagler College Students will represent the college properly. However, ideally, we would like to have a larger sample.
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 determined as large.
3. Big Population – Since 10n = (10)(150) = 1500 < 2500, the population is large, the total of Flagler students amounts to approximately 2500.
4. Independence within Sample – Yes, the sample is completely independent.
Compute
Result 3: One sample proportion summary hypothesis test – Married
One sample proportion summary hypothesis test:

Interpret
Since the pvalue (0.0019) 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 students are less likely to divorce.
Confidence Interval #1 – Estimating the Population Proportion
The hypothesis test shows that the majority of Flagler College students are less likely to divorce. Therefore, we will create a confidence interval for the students whose are identified as less likely. Since this is a onesided test with a significance level of 0.05 was run, we will use a 90% confidence interval test.
Prepare
0. Random Sample with Independent Observations – As far as we can determine, the sample is independent within its observations.
2. Large Sample – Since n*phat = (150)(0.6267) = 94.01 > 10 and n*(1 – phat) = (150)(1 – 0.6267) = (150)(0.3733) = 56 > 10, the sample is determined to be 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
Result 4: One sample proportion summary confidence interval – More/Less Likely
One sample proportion summary confidence interval:

Interpret
We are 90% confident that between 56.2% and 69.2% of all Flagler College students are less likely to divorce. This is most definitely the majority of all Flagler College students.
Hypothesis Test #2 – A Claim of the Difference between two Population Proportions
A contingency table was formed to compare the data collected from those that are more likely and less likely to divorce. Of the 94 less likely students, 49 of those students claimed that their parents were married. That makes 52.13% (49 students out of 94) of the less likely students and 60.71% (34 students out of 56) of the more likely students answered that their parents were still married. With an approximate14%difference in the percentages mentioned above, it seems as though our sample indicates that there are slight differences between students who are more likely and students who are less likely to get divorced even though their parents were married.
Result 5: Contingency table (with data) – More Likely Vs. Less Likely
Contingency table results:
ChiSquare test:

A hypothesis test will be used to identify the difference and statistical significance for the population of all Flagler College students. The test will again be run at a significance level of 0.05.
Hypothesize
Null: There is no difference in the proportion of the population of more likely students at Flagler College and the proportion of the population of less likely students at Flagler College whose parents are married.
Alternate: There is a difference in the proportion of the population of more likely students at Flagler College and the proportion of the population of less likely students at Flagler College whose parents are married.
Based on the alternate hypothesis, this is a two tailed test.
Prepare:
1. Large Samples – It is found that the collective sample proportion is
phat = (x_{1} + x_{2})/(n_{1} + n_{2}) = (49 + 45)/(67 + 83) = 94/150 = 0.6267
Sample One (Less Likely): Since n_{1}*phat = (94)(0.6267) = 58.9 > 10 and
n_{1}*(1  phat) = (94)(1 – 0.6267) = (94)(0.3733) = 35.1 > 10, sample one is large.
Sample Two (More Likely): Since n_{2}*phat = (56)(0.6267) = 35.1 > 10 and
n_{2}*(1  phat) = (56)(1 – 0.6267) = (56)(0.3733) = 21 > 10, sample two is large.
2. Random Samples – Again, probably not (but we hope they are representative). For now, we will make the assumption that the sample is random enough and represents all Flagler College Students fairly.
3. Independent Samples – Yes, the student responses were taken and fairly independent of one another.
4. Independence between Samples – Yes, there is no relationship between the students who are more likely and the students that are less likely to get divorced.
Compute
Result 6: Two sample proportion summary hypothesis test – Less Likely vs. Parents Not Married
Two sample proportion summary hypothesis test:

Difference 
Count1 
Total1 
Count2 
Total2 
Sample Diff. 
Std. Err. 
ZStat 
Pvalue 
p_{1}  p_{2} 
94 
150 
67 
150 
0.18 
0.057579575 
3.1261085 
0.0018 
Interpret
Since the pvalue, which is 0.0018, is less than the significance level of 0.05, the null hypothesis must be rejected. Remember, if the pvalue is low, the null must go! There is an ample amount of evidence that proves there is a difference between the portion population of less likely Flagler Students and the population proportion of more likely Flagler students whose parents are divorced.
Confidence Interval #2 –Estimate the Difference between two Population Proportions
The hypothesis test gave us, yet again, an abundance of evidence which determines that there is a difference between those whose parents are not married and less likely to get a divorce and those who are married and are likely to get a divorce. Therefore, we will create a confidence interval that again estimates the difference and optimistically will confirm these two population proportions cannot be identical. Since a two tailed test with a level of significance of 0.05 was tested, a 95% confidence interval will be generated.
Prepare
1. Random Samples with Independent Observations – Once again, the response that were taken were random and independent.
2. Large Samples –
Sample One (Less Likely Students): Since n_{1}*phat_{1} = (67)(0.7313) = 49 > 10 and
n_{1}*(1  phat_{1}) = (67)(1 – 0.7313) = (67)(0.2687) = 18 > 10, sample one is large.
Sample Two (More Likely Students): Since n_{2}*phat_{2} = (83)(0.5422) = 45 > 10 and
n_{2}*(1  phat_{2}) = (83)(1 – 0.5422) = (83)(0.4578) = 38 > 10, sample two is large.
3. Big Populations  Let’s assume its 50/50 between the two samples. We’ll split the population of students into tow groups, the total being 2500 students. There are roughly (0.50)(2500) = 1250 students who are more likely and (0.50)(2500) = 1250 students who are less likely in the population.
Population One (Less Likely Students): Since 10n_{1} = (10)(67) = 670 < 1250, population one is big.
Population Two (More Likely Students): Since 10n_{2} = (10)(83) = 830 < 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 7: Two sample proportion summary confidence interval – More Likely Vs. Parents Not Married
Two sample proportion summary confidence intervals:

Interpret
The confidence interval is half in the negative (that being the lower limit) and half in the positives (that being the upper limit); indicating that the percentage of the population of all more likely students whose parents are not married is less than the percentage population for students whose parents are not married and are less likely to divorce. That being said, we are 95% confident that the percentage of all More likely students whose parents are not married is between 11.6% and 10.3% less than the percentage of all students less likely to get divorced whose parents are not married.
Conclusion
Determining on if there is a difference between those who parents are married or not and if that is a decisionmaking factor for if students are more or less likely to get a divorce is a topic that should be discussed. In this report, the sample of 150 Flagler College students was given and then majority was identified as students who are less likely to get a divorce. We estimated that between 56.2% and 69.2% are less likely to get a divorce. Additionally, there was statistical evidence showing the students who were more likely to get divorced. Again, estimating that between 11.6% and 10.3% more of all college students believed that they’re more likely to get a divorce based on their parent’s marital status. The association between the two seems to be natural; but the evidence proves that there is a majority of Flagler College Students who are less likely to divorce despite their parent’s marital status.
The status on whether a student’s parents are married or not married should be associated with their parent’s marital status. The data, however, proves that students are not affected by their parent’s marital status. This allows us, the researchers, to be hopeful for the minority, the more likely, are able to make their own choices and not base them off their parents. People have argued that about 50% of all marriages end in divorce, if this is true then our statistical evidence in this phase has given us hope that the divorce rate will be much lower in the future.
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