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Created: Apr 25, 2019
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MAT223 Divorce Spring 2019: Tobiassen, Wallace, Wasserman Phase 3
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Introduction:

On the first phase of this project, we look at the status of 100 flagler college students who were enrolled in mat 223 parents marital status and various questions resulting from the main question.  In the second phase, this same sample of 100 students was divided into two smaller samples which were referred to as the students for who ongoing contact was important and those that didn’t. There are 83 Social Students and 17 Unsocial Students sampled.  A bar chart representing the two samples is presented below.

 

 



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 ongoing contact is important.  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 ongoing contact is important.

 

Second, the sample results will also be used to determine if the opinion of the population of all those students who believe that ongoing contact is important, and those students who don’t. 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 who think contact is important and those who don’t.

 

Hypothesis Test #1 – A Claim of Majority

In the sample of 100 students, 83  reported that ongoing contact is important.  That is, the majority, 83%, of the students sampled expressed that contact is important.  These sample results will be used to test the claim that the majority of the population of Flagler College students view ongoing contact as important 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 Ongoing contact is important

             Alternate: More than 50% of all Flagler College students believe that Ongoing contact is important

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 = (100) (0.50) = 50 > 10 and n(1-p0) = (100) (1-0.50) = 50> 10 are both true statements, the sample is large.

             3. Big Population – Since 10n = (10)(100) = 1000 < 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 (

 

Confidence Interval #1 – Estimating the Population Proportion

             The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that ongoing contact is important.  Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that ongoing contact is important  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 = (100)(0.83) = 83 > 10 and n*(1 – phat) = (100)(1 – 0.83) = 17 > 10, the sample is large.

             3. Big Population – Since 10n = (10)(100) = 100 < 2500, the population is big.  Recall, Flagler College has a population of appropriately 2500 students.

 

Compute

 

 

 

Interpret

We are 90% confident that between 76.82% and 89.17% of all Flagler College students find that ongoing contact is important. 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 students with divorced parents who saw ongoing contact as important.  Of the 83 Social Students, 17 felt ongoing contact was important. That is, 70.6% (12 students out of 17) of the students who did not think ongoing contact was important were more likely to divorce in the future and 41% (34 students out of the 83) students of the students who though ongoing contact was important wouldn’t get divorced in the future.  With an approximately 30% difference in these percentage, the sample gives some reason to believe that the population of Social Students at Flagler College and the population of students who don’t have ongoing contact at Flagler College differ in their opinion that weather they are going to get divorced in the future.

 

 

 

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 who won’t get divorced in the future at Flagler College and the proportion of the population of students who do not at Flagler College who feel social media is a distraction.

Alternate: There is difference in the proportion of the population of students who won’t get divorced in the future at Flagler College and the proportion of the population of students who do not at Flagler College who feel social media is a distraction

Based on the alternate hypothesis, this is a two tailed test.

Prepare:

1.      

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.

 

 

 

Interpret

Since the p – value = 0.0031 is less than the level of significance of 0.05, the null hypothesis will be rejected.  

 

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 students in favor of ongoing contact at Flagler College and the population of students who don’t have ongoing contact 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.

 

 

 

Interpret

This confidence interval is incases zero; this indicates that the percentage of the population of all students who aren’t in favor of ongoing contact is possibly the same than the percentage of the population of all students who aren’t in favor of ongoing contact.  Thus, I am 95% confident that the percentage of both groups is roughly equal.





Result 1: ongoing contact important phase 3   [Info]
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Result 2: ongoing contact phase 3   [Info]
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Result 3: One sample proportion summary hypothesis test (correct one)   [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
p831000.830.056.6<0.0001

Result 4: One sample proportion summary confidence interval .90   [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
p831000.830.037563280.76821390.8917861

Result 5: Contingency table (with data)   [Info]

Contingency table results:


Rows: Sample(Ongoing Contact Important)
Columns: Sample(More Likely to Divorce)
NoYesTotal
No12517
Yes493483
Total6139100

Chi-Square test:


StatisticDFValueP-value
Chi-square10.791505160.3736

Result 6: Two sample proportion summary hypothesis test (use this)   [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 = 0.5
HA : p1 - p2 ≠ 0.5

Hypothesis test results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.Z-StatP-value
p1 - p2121749830.115520910.12984754-2.96100410.0031

Result 7: Two sample proportion summary confidence interval (use this)   [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

90% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p2121749830.115520910.12298849-0.0867771650.31781898

Data set 1. MAT223 Divorce Spring 2019: Tobiassen, Wallace, Wa   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=87144">MAT223 Divorce Spring 2019: Tobiassen, Wallace, Wasserman Phase 3</A>

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