Teodoro A. Leo
August 17, 2019
Stats
PHASE THREE: Flagler College Students and Reading Styles Spring 2019
Introduction:
On the first phase of this project, the reading styles of a sample of 150 Flagler College students from the spring semester 2019 was explored. In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as the “did not” and the “did”. The term “Did not” defined the sample of those Flagler College students who do not think reading helps with social skills and the term “did” defined the sample of those Flagler College students who do think reading helps social skills. There are 70 “did not” and 80 “did” 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 their reading styles and if reading helps their social skills.
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 reading helps with social skills. 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 reading does help social skills. Second, the sample results will also be used to determine if the opinion of the population of all “did not” and the population of all “did” at Flagler College have a statistically significant difference of opinion regarding if reading helps with social skills. 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 “did not” and “did” who find reading to be helpful in social skills.
Hypothesis Test #1 A Claim of Majority
In the sample of 150 students, 80 reported that reading does help with social skills. That comes out to be 53.33% of the students sampled expressed that reading does help with social skills. These sample results will be used to test the claim that the majority of the population of Flagler College students view reading helpful to social skills at a level of significance of 0.05 A pie chart of the data is given below.
Confidence Interval #1 Estimating a Population Proportion
Hypothesize
Null: Fifty percent of all Flagler College students believe that reading is helpful to their development of social skills.
Alternate: More than 50% of all Flagler College students believe that reading is helpful to their development of social skills.
Based on the alternate hypothesis, this is a rightsided test.
Prepare
1. Random Sample – Maybe— but we hope it is representative. However, to proceed, we will assume it is.
2. Large Sample – Since np_{0} = (150) (0.50) = 80 > 10 and n(1p_{0}) = (150) (0.50) = 80 > 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.
One sample proportion summary hypothesis test:p : Proportion of successes H_{0} : p = 0.5 H_{A} : p > 0.5 Hypothesis test results:

Interpret
Since the pvalue (0.2071) is more than the level of significance of 0.05, the null hypothesis must stay. Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students feel that reading helps with social skills.
The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that reading helps with social skills. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that reading is helpful to their social skills. Since a onetailed 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, maybe—but we hope it is representative. To proceed, we will assume it is. 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)(0.5333) = 80 > 10 and n*(1 – phat) = (150)(1 – 0.5333) = (150)(0.4667) = 70 > 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
One sample proportion summary confidence interval:p : Proportion of successes Method: StandardWald 90% confidence interval results:

Interpret
We are 90% confident that between 46.6% and 60.0% of all Flagler College students find that reading helps with social skills. This is certainly not a majority of all Flagler College students. since our numbers cross between the 50% mark.
Hypothesis Test #2 A claim of the Difference Between Two Population Proportions
A contingency table was created to compare the gender of the “did not” and the “did” students regarding the helpfulness of reading in regards to better social skills. Of the 80 “did” students, 53 were female while 27 were male. Of the 70 “did not” students, 51 were female, while 19 were male. This would make sense since Flagler College has a higher female population than the male population.
Contingency table results:Rows: Social Skills Columns: Gender
ChiSquare test:

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 female students at Flagler College and the proportion of the population of male students at Flagler College who feel reading is helpful to social skills.
Alternate: There is a difference in the proportion of the population of female students at Flagler College and the proportion of the population of male students at Flagler College who feel reading is helpful to social skills.
Based on the alternate hypothesis, this is a twotailed test.
Prepare:
1. Large Samples – It is found that the pooled sample proportion is
phat = (x_{1} + x_{2})/(n_{1} + n_{2}) = (53 + 51)/(19 + 27) = 4784/150 = 31.8933
Sample One (female): Since n_{1}*phat = (53)(31.8933) = 57.8 > 10 and
n_{1}*(1  phat) = (19)(1 – 31.8933) = (19)(30.8933) = 23.2 > 10, sample one is large.
Sample Two (male): Since n_{2}*phat = (51)(31.8933) = 49.25 > 10 and
n_{2}*(1  phat) = (27)(1 – 31.8933) = (27)(30.8933) = 19.8 > 10, sample two is large.
2. Random Samples – Again, maybe—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.
Two sample proportion summary hypothesis test:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions H_{0} : p_{1}  p_{2} = 0 H_{A} : p_{1}  p_{2} ≠ 0 Hypothesis test results:

Interpret
Since the pvalue = 0.3813 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 female students at Flagler College and the proportion of the male students at Flagler College who feel reading helps with social skills.
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 gender opinion that reading helps with social skills. Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions cannot be equal. Since a twotailed 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—to proceed, we will assume it is. Yes, the student responses were taken in such a way that their responses were independent of each other.
2. Large Samples –
Sample One (female): Since n_{1}*phat = (53)(31.8933) = 57.8 > 10 and
n_{1}*(1  phat) = (19)(1 – 31.8933) = (19)(30.8933) = 23.2 > 10, sample one is large.
Sample Two (male): Since n_{2}*phat = (51)(31.8933) = 49.25 > 10 and
n_{2}*(1  phat) = (27)(1 – 31.8933) = (27)(30.8933) = 19.8 > 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 regarding social skills by reading, we will assume 50% is and 50% are not. Hence, there are approximately (0.50)(2500) = 1250 students who “did not” and (0.50)(2500) = 1250 students who are “did” in the population.
Population One (did not): Since 10n_{1} = (10)(70) = 700 < 1250, population one is big.
Population Two (did): Since 10n_{2} = (10)(80) = 890 < 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.
Two sample proportion summary confidence interval:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions 95% confidence interval results:

Interpret
This confidence interval contains 0; this indicates that there is no statistically meaningful or statistically significant difference between the groups. Thus, I am 95% confident that the percentage of all who feel social media causes a distraction is between 8.09% and 21.30%.
Conclusion
Society still believes that reading helps enhance social skills—with a surprising finding that an overwhelming majority still prefers a physical book when reading, In this report, the sample pro divide evidence that more of Flagler College students find reading helps with social skills. It is interesting to note that even though there are more women participating in this survey (which makes sense regarding Flagler's population) that the stats showed that women and men didn’t differ much at all in their opinion. The only time we saw a more spread diverse opinion was when we were looking at age—it showed that the older you were the more likely you would say that reading enhanced your social skills—and that you read more often for fun. Hopefully, younger generations will continue to hold onto reading for fun and not let it disappear with the rise of social media and such.
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