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PHASE THREE: Flagler College Students and Reading Styles
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PHASE THREE: Flagler College Students and Reading Styles


Introduction:


On the first phase of this project, the reading habits of students attending Flagler College was explored. In the second phase, this sample of 150 students was divided into two smaller samples that explored whether or not these students believe reading improves their social skills. This sample is titled “social skills” and those who do think reading improve their social skills are called “social students”, while those who do not think reading improves their social skills are called “unsocial students”. 74 students do not think reading improves their social skills, and 76 students do think reading improves their social skills. This result is displayed in the pie chart below.


Result 1: Social Skills.   [Info]
Right click to copy


On this phase of the report, we will explore students’ opinions over whether reading for pleasure has decreased for our generation.


First, we will use methods of statistical inference to determine if the sample results indicate that the majority of the population of all Flagler College students believe reading for pleasure has decreased for our generation. We will first run a hypothesis test in order to find statistical evidence of majority, and then we will create a confidence interval to estimate the percentage of the population of Flagler College students who believe reading for pleasure has decreased.


Second, the sample results will be used to determine if the opinions regarding reading for pleasure is statistically significantly different from antisocial students at Flagler College. 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 social and unsocial students who believe reading for pleasure has decreased for our generation.


Hypothesis Test #1 - A Claim of Majority


In our sample of 150 students, 131 reported that they think that reading for pleasure has decreased for our generation as opposed to older generations. Therefore, the majority of students, 87.33%, believe reading for pleasure has decreased.  These sample results will be used to test the claim that the majority of the population of Flagler College students believe reading for pleasure has decreased at a level of significance of 0.05  A pie chart of the data is given below.


Result 2: Reading for Pleasure.   [Info]
Right click to copy

Hypothesize


Null: 50% of all Flagler College Students believe that reading for pleasure has decreased for our generation as opposed to older generations.

Alternate: More than 50% of all Flagler College Students believe that reading for pleasure has decreased for our generation as opposed to older generations.


Prepare


  1. Random Sample- While it is most likely not a true random sample, we will proceed by assuming it is.


  1. Large Sample- Since np0 =  (150) (0.50) = 75 > 10 and n(1-p0) = (150) (0.50) = 75 > 10 the sample is large and the condition is met.


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


  1. Independence Within Sample- Yes, the student responses were taken in such a way that their responses were independent of each other.


Compute

Result 3: One sample proportion summary hypothesis test   [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
p1311500.873333330.0408248299.1447617<0.0001


Interpret


Since the p-value (<0.0001) is less than the 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 believe that reading for pleasure has decreased for our generation as opposed to older generations.


Confidence Interval #1 - Estimating the Population Proportion


The hypothesis test gives us sufficient evidence that the majority of all Flagler College students believe that reading for pleasure has decreased for our generation. Therefore a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that reading for pleasure has decreased. 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, while it is most likely not a true random sample, we will proceed by assuming it is. Furthermore, yes, the student responses were taken in such a way that their responses were independent of each other.


  1. Large Sample- Since n(p-hat) = (150)(.8733) = 131 >  10 and n(1 - p-hat) = 150 (1 - 0.8733) = (150)(.1267) = 19 >10, the sample is large.


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


Compute


Result 4: One sample proportion summary 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
p1311500.873333330.027156610.828664680.91800198


Interpet


We are 90% confident that between 82.87% and 91.8% of all Flagler College students believe that reading for pleasure has decreased for our generation. This is definitely 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 social students and the unsocial students regarding whether reading for pleasure has decreased. Of the 76 social students, 67 believed that reading for pleasure had decreased (88.16%), and of the 74 unsocial students, 64 believed that reading for pleasure had decreased (86.48%). With a difference of only 1.68%, this sample does not give us reason to believe that the opinions regarding whether or reading for pleasure has decreased for our generation differ significantly for students who do or do not read for pleasure at Flagler College.


Result 5: Contingency table (with data) - Social Skills and Reading for Pleasure   [Info]
Contingency table results:
Rows: Social Skills
Columns: Reading for Pleasure
NoYesTotal
No106474
Yes96776
Total19131150

Chi-Square test:
StatisticDFValueP-value
Chi-square10.0946840350.7583


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 social and unsocial students at Flagler College who believe that reading for pleasure has decreased for our generation opposed to older generations.

Alternate: There is a difference in the proportion of the population of social and unsocial students at Flagler College who believe that reading for pleasure has decreased for our generation opposed to older generations.


Prepare:

  1.  Large Samples – It is found that the pooled sample proportion is


p-hat = (x1 + x2)/(n1 + n2) = (64 + 67)/(74 + 76) = 131/150 = .8733


Sample One (social students): Since n1*p-hat = (76)(0.8733) = 66.37 > 10 and


n1*(1 - p-hat) = (76)(1 – 0.8733) = (76)(0.1267) = 9.62 < 10, sample one is not large, but we will proceed anyway.


Sample Two (unsocial students): Since n2*p-hat = (74)(0.8733) = 64.62 > 10 and


n2*(1 - p-hat) = (74)(1 – 0.8733) = (74)(0.1267) = 9.38 < 10, sample two is not large, but we will proceed anyway.


  1. Random Samples – Again, probably not (but we hope they are representative).  However, to proceed, we will assume they are.


  1. Independent Samples – Yes, the student responses were taken in such a way that their responses were independent of each other.  


  1. Independence between Samples – Yes, there is no relationship between the social students and the unsocial students.


Compute


Result 6: Two sample proportion summary hypothesis test   [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 - p2677664740.0167140830.0543180490.307707710.7583


Interpret


Since the p – value = 0.7583 is greater than the level of significance of 0.05, we will fail to reject the null hypothesis. Therefore, there is not sufficient evidence to suggest a difference in the proportion of the population of social and unsocial students at Flagler College who believe that reading for pleasure has decreased for this generation as opposed to older generations.



Confidence Interval #2 - Estimate the Difference Between Two Population Proportions


The hypothesis test gave us sufficient evidence that there is not a significant difference between social students at Flagler College and the population of unsocial students at Flagler College in the belief that reading for pleasure has decreased. Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions can 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.


  1. Large Samples


Sample One (social students): Since n1*p-hat1 = (76)(0.882) = 67 > 10 and


n1*(1 - p-hat1) = (76)(1 – 0.882) = (76)(0.118) = 9 < 10, sample one is not large, however we will proceed anyway.


Sample Two (unsocial students): Since n2*p-hat2 = (74)(0.865) = 64 > 10 and


n2*(1 - p-hat2) = (74)(1 – 0.865) = (74)(0.135) = 10 > 10, sample two is large.


  1. Big Populations – Flagler College has a population of appropriately 2500 students. Since we are unsure what overall percentage of the students do or do not believe that reading for pleasure has decreased over time, we will assume 50% do believe this, and 50% do 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 (Social Students): Since 10n1 = (10)(76) = 760 < 1250, population one is big.


Population Two (Unsocial Students): Since 10n2 = (10)(74) = 740 < 1250, population two is big.


  1. 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   [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 - p2677664740.0167140830.054341741-0.0897937720.12322194


Interpret


This confidence interval contains zero; this indicates that the percentage of the population of all social students who feel believe reading for pleasure has decreased over time may be equal to the percentage of the population of all unsocial students who believe reading for pleasure has decreased over time. Therefore, because the confidence interval is -0.0898 and .1232,  we are 95% confident that there is no statistical difference between social and unsocial students who believe that reading for pleasure has decreased over time.



Conclusion


This report provided evidence that suggests that the majority of all Flagler College students believe that reading for pleasure has decreased over time for our generation as opposed to older generations.  There was no difference in this opinion between students who believe that reading improves their social skills, and students who do not believe that reading improves their social skills. It is not surprising that there is no difference in opinion because I feel that it has become quite obvious that reading for pleasure is not a very common past time anymore. This is likely due to the fact that certain technological advancements, such as smartphones, have come to replace books in more ways than one.


It is not inherently a negative thing that smartphones have become commonplace, in fact it shows how far our society has come. However, a negative consequence of this replacement is a lack of appreciation for literature, and therefore a less informed society. If we continue to place more value in technology, as opposed to books, it is likely that reading for pleasure will not only decrease over time, it will become a rarity.


Data set 1. Flagler College Students and Reading Styles - Mari   [Info]
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<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=82732">PHASE THREE: Flagler College Students and Reading Styles</A>

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