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Created: Dec 7, 2018
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Phase 3: Flagler College Students and Divorce
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Introduction:

On the first phase of this project, the opinions on marriage and divorce were explored with a sample of 150 Flagler College students from fall semester 2018.  In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as the Parent still married and parents divorced.  The term “parents married” defined the sample of those Flagler College students whose parents are still married and the term “parents divorced” defined the sample of those Flagler College students whose parents are divorced.  There are approximately 47 parents married Students and approximately 53 parents divorced 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 if they are more likely to divorce if their parents are.

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 divorced parents will cause them to divorce as.  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 social media is a distraction.

Second, the sample results will also be used to determine if the opinion of the population of all parents still married students and parents divorced students at Flagler College have a statistically significant difference of opinion regarding getting a divorce caused by their own parents being divorced.  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 parents married Students and parents divorced Students who find that having divorced parents will cause them to get a divorce themself.

Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 79 reported that they are more likely to divorce.  That is, the majority, 52.67%, of the students sampled expressed that they are more likely to divorce.  These sample results will be used to test the claim that the majority of the population of Flagler College students view that the fact that there parents are divorced will mean that they will get divorced as well 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 with divorced parents they are more likely to divorce.

              Alternate: More than 50% of all Flagler College students believe that with divorced parents the are more likely to get divorced.

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

 

 

Interpret

Since the p-value (0.2568) is more than the level of significance of 0.05, the null hypothesis is not rejected.  Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students feel that having divorced parents will lead them to getting a divorce.

Confidence Interval #1 – Estimating the Population Proportion

              The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that having divorced parents will lead them to getting a divorce.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that social media is a distraction to their day.  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)(0.5267) = 80 > 10 and n*(1 – phat) = (150)(1 – 0.5267) = (150)(0.4733) = 71 > 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

 

Interpret

We are 90% confident that between 46% and 59.4% of all Flagler College students find that having divorced parents will lead them to getting a divorce. 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 Parents married Students and the parents divorced Students regarding the students with parents that are divorced will mean that they will get divorced as well.  Of the 71 parents not married Students, 27 felt that the will get a divorce and of the 79 Parents divorced Students, 34 said that they will get divorced. That is, 38% (27 students out of 71) of the parents married Students felt that they will get divorced and 43% (34 students out of the 79 students) of the divorced parents Students felt that they would get divorced.  With an approximately 5% difference in these percentage, the sample gives some reason to believe that the population of parents married Students at Flagler College and the population of parents divorced Students at Flagler College differ slightly in their opinion that if their parents are divorced will mean that they will get divorced as well.

 

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 Parents married Students at Flagler College and the proportion of the population of parents divorced Students at Flagler College who feel that if their parents are divorced will mean that they will get divorced as well.

Alternate: There is a difference in the proportion of the population of Parents married Students at Flagler College and the proportion of the population of parents divorced Students at Flagler College who feel that’s if parents are divorced will mean that they will get divorced as well.

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) = (27 + 34)/(71 + 79) = 61/150 = 0.4733

Sample One (Parents married Students): Since n1*p-hat = (71)(0.4733) = 33.6 > 10 and

n1*(1 - p-hat) = (71)(1 – 0.4733) = (71)(0.5267) = 37.4 > 10, sample one is large.

Sample Two (parents divorced Students): Since n2*p-hat = (79)(0.4733) = 37.4 > 10 and

n2*(1 - p-hat) = (79)(1 – 0.4733) = (79)(0.5267) = 41.6 > 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 Social Students and the Unsocial Students.

 

Compute

 

 

Interpret

Since the p – value = 0.5328 is more than the level of significance of 0.05, the null hypothesis will not be rejected.  Therefore, there is sufficient evidence that there exists a difference in the proportion of the population of parents married Students at Flagler College and the proportion of the population of parents divorced Students at Flagler College who feel that if their parents are divorced will mean that they will get divorced as well.

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 social media is a distraction between the population of Social Students at Flagler College and the population of Unsocial 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 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 – It is found that the pooled sample proportion is

p-hat = (x1 + x2)/(n1 + n2) = (27 + 34)/(71 + 79) = 61/150 = 0.4733

Sample One (Parents married Students): Since n1*p-hat = (71)(0.4733) = 33.6 > 10

and

n1*(1 - p-hat) = (71)(1 – 0.4733) = (71)(0.5267) = 37.4 > 10, sample one is large.

Sample Two (parents divorced Students): Since n2*p-hat = (79)(0.4733) = 37.4 > 10 and

n2*(1 - p-hat) = (79)(1 – 0.4733) = (79)(0.5267) = 41.6 > 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 (parents married Students): Since 10n1 = (10)(71) = 710 < 1250, population one is big.

Population Two (parents divorced Students): Since 10n2 = (10)(79) = 790 < 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

 

 

Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all parents married Students who feel that is their parents are divorced will mean that they will get divorced as well  is less than the percentage of the population of all parents divorced Students who feel that is their parents are divorced will mean that they will get divorced as well.  Thus, I am 95% confident that the percentage of all parents divorced Students who feel that is their parents are divorced will mean that they will get divorced as well is between -20.7% and 10.7% greater than the percentage of all parents married Students who feel that is their parents are divorced will mean that they will get divorced as well.

Conclusion

Society has embraced that there is a extremely high rate for divorce In this report, the sample provided evidence that the majority of all Flagler College students find that if their parents are divorced will mean that they will get divorced as well.  In fact, it was estimated that between 38% and 43% of all Flagler College students find that that is their parents are divorced will mean that they will get divorced as well.  Furthermore, it was found that there is statistical evidence that those students who feel having married parents makes them more likely to divorce.  It was estimated that between   -20.7% and 10.7% more of all Flagler College students whose parents are divorced feel they are more likely to divorce than all other Flagler College students.  I feel that with the average divorce rate for couples being 50% more people believe in the negative outcome to relationships making them believe that they have a high chance of divorce. I too am I the category that I feel that I have an extreme chance of divorce thus it will probably take me a long time with someone in order for me to marry them. I don’t know how one would go about trying to prevent couple from divorcing because it is such a personal thing. I say this because I don’t think anyone has the right to tell someone how to live their own life unless the situations are an endangerment to someone’s life.

 

 

 


Result 1: Bar Plot With Data married vs not married   [Info]
Right click to copy

Result 2: Pie Chart With Data   [Info]
Right click to copy

Result 3: One sample proportion summary hypothesis test-more likely to divorce   [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
p791500.526666670.0408248290.653197260.2568

Result 4: One sample proportion summary confidence interval- more likely to divorce   [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
p791500.526666670.0407667260.459611370.59372196

Result 5: Contingency table Married vs More likely to divorce   [Info]

Contingency table results:


Rows: (Married)
Columns: (More Likely to Divorce)
NoYesTotal
No442771
Yes453479
Total8961150

Chi-Square test:


StatisticDFValueP-value
Chi-square10.388954340.5328

Result 6: Two sample proportion summary hypothesis test of students whos parents are divorced and that they wi   [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 - p227713479-0.0500980570.080328854-0.623662040.5328

Result 7: Two sample proportion summary confidence interval students whose parents are divorced and likely to   [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 - p227713479-0.0500980570.080140275-0.207170110.106974

Data set 1. Flagler College Students and Divorce - Ayotte, Mun   [Info]
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