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Created: Dec 7, 2018
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PHASE 3: Flagler College Students and Divorce - Lampp, Palmieri, Porto
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Introduction:

In the first phase of this project, a group  150 statistics students at Flagler College in the Fall 2018 semester were surveyed on divorce. The data was self reported and for a particular group of students which could make this data biased. In phase two of this project, the sample of 150 students was divided into two groups. The two samples are the sample of Flagler College students who have parents that are married and Flagler College students whose parents are not married. There are 65 Flagler College students with parents who are not married and 85 Flagler College students with parents who are married. A pie chart representing these results is below.

 

In this phase of the report, attention will be brought to whether or not students believe that they are more likely to get divorced later on in life if their parents are divorced.


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 who believe that they are more likely to get divorced later on in life. 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 believe they will get divorced later in life.

Second, the sample results will also be used to determine if the opinion of the population of all students who have divorced parents at Flagler College have a statistically significant difference of opinion on if they believe they will be divorced later in life. 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 students at Flagler College who believe that they will be divorced later in life.

 

Do you think that children of divorced parents are more likely to divorce themselves later in life?


Hypothesis test 1 – A claim of majority :

In the sample of 150 students, 96 reported that they believe children of divorced parents are not more likely to divorce themselves later on in life.  That is, the majority, 64%, of the students sampled expressed that they do not think children of divorced parents are more likely to divorce themselves. These sample results will be used to test the claim that the majority of the population of Flagler College students view divorce rates among children with divorced parents at a level of significance of 0.05  A pie chart of the data is given below.


Hypothesize

Null Hypothesis: 50% of all Flagler College students believe that children of divorced parents are not more likely to divorce themselves later on in life.

Alternative Hypothesis: More than 50% of all Flagler College students believe that children of divorced parents are not more likely to divorce themselves later on in life.

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 (0.0003) 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 do not feel that children of divorced parents will get divorced later on in life.

 

Confidence Interval #1 – Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that children of divorced parents will not get divorced later on in life. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that children of divorced parents will not get divorced later on in life. 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)(0.64) = 96 > 10 and n*(1 – phat) = (150)(1 – 0.64) = (150)(0.36) = 54 > 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 57.6% and 70.4% of all Flagler College students find that students with divorced parents are not more likely to divorce later on in life.  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 students with married parents and students with divorced parents regarding the importance of ongoing contact.  Of the 65 students whose parents are not married, 48 felt ongoing contact is important for divorced parents. And of the 85 students with married parents, 78 felt ongoing contact was important for divorced parents.  That is, 73.8% (48 students out of 65) of the students with divorced parents felt ongoing contact is important and 91.8% (78 students out of the 85 students) of the students with married parents felt ongoing contact is important.  With an approximately 20% difference in these percentage, the sample gives some reason to believe that the population of students with married parents at Flagler College and the population of students with divorced parents at Flagler College differ in their opinion that ongoing contact is important.

 

 

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 students with married parents at Flagler College and the proportion of the population of students with divorced parents at Flagler College who feel ongoing contact between divorced parents is important.

Alternate: There is a difference in the proportion of the population of students with married parents at Flagler College and the proportion of the population of students with divorced parents at Flagler College who feel ongoing contact is important.

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) = (48 + 78)/(65 + 85) = 126/150 = 0.84

Sample One (students with married parents): Since n1*p-hat = (126)(0.84) = 105.84 > 10 and

n1*(1 - p-hat) = (126)(1 – 0.84) = (126)(0.16) = 20.16 > 10, sample one is large.

Sample Two (students with divorced parents): Since n2*p-hat = (24)(0.84) = 20.16 > 10 and

n2*(1 - p-hat) = (24)(1 – 0.84) = (24)(0.16) = 3.84 < 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 students with married parents and students with divorced parents.

 

 

 

Interpret

Since the p – value =

 

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 ongoing contact between divorced parents is important between the population of students with married parents at Flagler College and the population of students with divorced parents 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

Sample One (Social Students): Since n1*p-hat1 = (24)(0.593) = 14.232 > 10 and

n1*(1 - p-hat1) = (24)(1 – 0.593) = (24)(0.407) = 9.768 < 10, sample one is not large.

Sample Two (Unsocial Students): Since n2*p-hat2 = (48)(0.855) = 41.04> 10 and

n2*(1 - p-hat2) = (48)(1 – 0.855) = (48)(0.145) = 6.96 < 10, sample two is not 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 divorced parents, we will assume 50% are and 50% are not.  Hence, there are approximately (0.50)(2500) = 1250 students who are students with divorced parents and (0.50)(2500) = 1250 students who are students with married parents in the population.

Population One (students with married parents): Since 10n1 = (10)(14.2) = 142 < 1250, population one is big.

Population Two (students with divorced parents): Since 10n2 = (10)(41) = 410 < 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.

 

< result 7 >

 

Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all students with married parents who feel ongoing contact between divorced parents is important is less than the percentage of the population of students with divorced parents who feel ongoing contact between divorced parents is important.  Thus, I am 95% confident that the percentage of all students with married parents who feel ongoing contact between divorced parents is important is between 43.4% and 64% greater than the percentage of all students with married parents that feel ongoing contact is important.

 

 

Conclusion:

In this report, the sample provided evidence that the majority of all Flagler College students believe that students with divorced parents are not more likely to divorce. In fact, we are 90% confident that between 57.6% and 70.4% of all Flagler College students find that students with divorced parents are not more likely to divorce later on in life. Also, it was found that there is statistical evidence that those students who have divorced parents and believe ongoing contact is important.  We are 95% confident that the percentage of all students with married parents who feel ongoing contact between divorced parents is important is between 43.4% and 64% greater than the percentage of all students with married parents that feel ongoing contact is important.

 

Result 1: Are Your Parents Married or Divorced   [Info]
Right click to copy

Result 2: Contingency table - Is Ongoing Contact Important   [Info]
Contingency table results:
Rows: Married or Not
Columns: Is Ongoing Contact Important
NoYesTotal
No174865
Yes77885
Total24126150

Chi-Square test:
StatisticDFValueP-value
Chi-square18.79928890.003

Result 3: Contingency table - Should You Stay Married For Your Kids   [Info]
Contingency table results:
Rows: Married or Not
Columns: Should You Stay Married for Kids
NoYesTotal
No58765
Yes751085
Total13317150

Chi-Square test:
StatisticDFValueP-value
Chi-square10.0363231740.8488

Result 4: Summary statistics for Number of Years Parents have been Married:   [Info]
Summary statistics for Number of Years Parents have been Married:
Group by: Married or Not
Married or NotnMinQ1MedianQ3MaxIQR
No650210203618
Yes850212527506

Data set 1. Flagler College Students and Divorce - Lampp, Palm   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82836">PHASE 3: Flagler College Students and Divorce - Lampp, Palmieri, Porto</A>

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