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PHASE THREE: Cell phones and Flagler College Students in Spring 2019 - Thompson/Wallace/Blonski
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PHASE THREE: Cell phones and Flagler College Students in Spring 2019 - Thompson/Wallace/Blonski 

 

Introduction: 

On the first phase of this project, the opinions on Cell Phone usage of a sample of 150 Flagler College Students was explored. In the second phase, this sample of 150 students was divided into two smaller samples. These samples were referred to as Important, or students who believed that social media is important to your social life to always be “connected” via your cell phone, and Not Important, or students who believed that social media is not important to your social life to always be “connected” via your cell phone. According to the survey, there are 83 Important students and 67 Not important students sampled. A bar chart representing the two samples is presented below. 

Result 1: Important and Not Important Students Sampled 

<result1> 

On this phase of the report, attention will be given to students’ opinions on whether or not social media is addictive.  

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 cell phones are addictive. 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 cell phones use is addictive.  

Second, the sample results will also be used to determine if the opinion of the population of all Not Important students at Flagler College have a statistically significant difference of opinion regarding the addictiveness of cell phones. Essentially, 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 Important and Not Important students who find cell phone use to be addictive.  

Hypothesis Test #1 – A Claim of Majority 

 
 

In the sample of 150 students, 137 reported that cell phone use is addictive. That is the majority, 91.33% of the students sampled expressed that cell phone use is addictive. These sample results will be used to test the claim that the majority of the population of Flagler College students view cell phone usage as addictive at a significance level of 0.05. A pie chart of the data is given below.  

 

<result2> 

 
Hypothesize  

Null: Fifty percent of all Flagler Students believe that cell phone usage is addictive. 

Alternate: More than fifty percent of all Flagler Students believe that cell phone usage is addictive.  

Based on the Alternate Hypothesis this is a right sided test.  

Prepare 

  1. Random Sample- Likely not 100% random (the survey was an assignment for math students, but hopefully it is somewhat representative).  However, to proceed, we will assume it is. 

  1.               2. Large Sample – Since np0 = (150) (0.50) = 75 > 10 and n(1-p0) = (150) (0.50) = 75 > 10 are both true statements, it is a sufficiently large sample. 

  1.               3. Big Population – Since 10n = (10)(150) = 1500 < 2700, the population is big.  Recall, Flagler College has a population of appropriately 2700 students currently enrolled. 

  1.               4. Independence within Sample – Yes, the student responses in the survey were taken in such a way that their responses were ultimately independent of each other. 

 

Compute 

 

Result 3: One sample proportion summary hypothesis test – Addictive  

p : Proportion of successes 
H0 : p = 0.5 
HA : p > 0.5 
 
Hypothesis test results: 
 

Proportion 

Count 

Total 

Sample Prop. 

Std. Err. 

Z-Stat 

P-value 

p 

137 

150 

0.91333333 

0.040824829 

10.124558 

<0.0001 
 
 

 

Since the p-value (<0.0001) is less than the level of significance of 0.05, the null hypothesis that exactly half of Flagler College students support recreational marijuana use must be rejected.  Therefore, there is sufficient evidence to support the claim that the majority, or more than half, of all Flagler College students feel that cell phone usage is addictive.  

Confidence Interval #1 – Estimating the Population Proportion 

              The hypothesis test gives sufficient evidence that more than 50%, or the majority, of all Flagler College students feel that cell phone usage is addictive. Since this is true, a confidence interval will now be created in order to estimate the percent of the population of all Flagler College students who feel that cell phone usage is addictive. 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 – Once more, the sample is not likely 100% random (but we hope it is representative).  However, to proceed, we will again assume it is.  

As for having Independent responses, 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)(0.913) = 137 > 10 and n*(1 – phat) = (150)(1 – 0.913) = (150)(0.087) = 13 > 10, the sample is considered large. 

              3. Big Population – Since 10n = (10)(150) = 1500 < 2700, the population is big.  Again, Flagler College has a population of appropriately 2700 students. 

 

Result 4: One sample proportion summary confidence interval – Addictive  

One sample proportion summary confidence interval: 

 
p : Proportion of successes 
Method: Standard-Wald 
 
90% confidence interval results: 
 

Proportion 

Count 

Total 

Sample Prop. 

Std. Err. 

L. Limit 

U. Limit 

p 

137 

150 

0.91333333 

0.022971802 

0.87554808 

0.95111859 

 

Interpret 

We are 90% confident that between 87.6% and 95.1% of all Flagler College students find that cell phone usage is addictive. Therefore, 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 Important and Not Important regarding the addiction of cell phone usage. Of the 67 Not Important students 57 of them felt that cell phone usage is addictive and of the 83 Important students, 80 of them felt that cell phone usage is addictive . That is 85.07% (57/67) of the Not Important students feel cell phone usage is addictive while 96.39% (80/83) of the Important students feel that cell phone usage is addictive. With an approximately 11% difference in these percentage, the sample gives some reason to believe that the population of Important Students at Flagler College and the population of Not Important Students at Flagler College differ in their opinion that cell phone usage is addictive.  

Result 5: Contingency table (with data) - Important vs Addictive  

Rows: Important to your social life to always be “connected” via your cell phone 
Columns: Believe that cell phone use is addictive 
 

 

No 

Yes 

Total 

No 

10 

57 

67 

Yes 

3 

80 

83 

Total 

13 

137 

150 

 
Chi-Square test: 

Statistic 

DF 

Value 

P-value 

Chi-square 

1 

5.9920542 

0.0144 

 
 

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 Important Students at Flagler College and the proportion of the population of Not Important Students at Flagler College who feel that cell phone usage is addictive.  

  

Alternate: There is a difference in the proportion of the population of Important Students at Flagler College and the proportion of the population of Not Important Students at Flagler College who feel cell phone usage is addictive.  

  

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) = (57+ 80)/(67 + 83) = 137/150 = 0.91 

Sample One (Important): Since n1*p-hat = (67)(0.91) = 60.97 > 10 and 

n1*(1 - p-hat) = (67)(1 – 0.91) = (67)(0.09) = 6.03 < 10, sample one is not large. 

Despite the sample not being large enough the analysis will proceed assuming that the sample is large enough.  

Sample Two (Not Important): Since n2*p-hat = (83)(0.91) = 75.53 > 10 and 

n2*(1 - p-hat) = (83)(1 – 0.91) = (81)(0.09) = 7.29 < 10, sample two is not large. 

Once again the sample is not large enough the analysis will proceed assuming the sample is large enough. 

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 known relationship between the Important Students and the Not Important Students. 

Compute 

Result 6: Two sample proportion summary hypothesis –  

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: 
 

Difference 

Count1 

Total1 

Count2 

Total2 

Sample Diff. 

Std. Err. 

Z-Stat 

P-value 

p1 - p2 

57 

67 

80 

83 

-0.11310915 

0.046207224 

-2.4478673 

0.0144 

 
Interpret 

Since the p – value = 0.0144 is less than the level of significance of 0.05, the null hypothesis will be rejected.  Therefore, there is sufficient evidence that there exists a difference in the proportion of the population of Important Students at Flagler College and the proportion of the population of Not Important Students at Flagler College who feel that cell phone usage is addictive.  

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 cell phone usage is addictive between the population of Important Students at Flagler College and the population of Not Important 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 –  

Sample One (Important Students): Since n1*p-hat1 = (67)(0.8507) = 57 ≥ 10 and 

n1*(1 - p-hat1) = (67)(1 – 0.8507) = (67)(0.1493) = 10 ≥ 10, sample one is large. 

Sample Two (Not Important Students): Since n2*p-hat2 = (83)(0.9639) = 77 ≥ 10 and 

n2*(1 - p-hat2) = (83)(1 – 0.9639) = (83)(0.0361) = 3 ≤ 10, sample two is not large. 

Once again the sample is not large enough the analysis will proceed assuming the sample is large enough.  

3. Big Populations – Recall, Flagler College has a population of appropriately 2700 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)(2700) = 1350 students who are Important Students and (0.50)(2700) = 1350 students who are Not Important Students in the population. 

Population One (Important Students): Since 10n1 = (10)(67) = 670 < 1250, population one is big.  

Population Two (Not Important Students) Since 10n2 = (10)(83) = 830 < 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: Two sample proportion summary confidence interval 

 
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: 
 

Difference 

Count1 

Total1 

Count2 

Total2 

Sample Diff. 

Std. Err. 

L. Limit 

U. Limit 

p1 - p2 

57 

67 

80 

83 

-0.11310915 

0.048113581 

-0.20741004 

-0.018808268 

 
 

 
This confidence interval is completely negative; this indicates that the percentage of the population of all Important Students who feel cell phone usage is less than the percentage of the population of all Not Important Students who feel cell phone usage is addictive.  Thus, I am 95% confident that the percentage of all Important Students who feel cell phone usage causes addiction is between 18.8% and 20.7% greater than the percentage of all Important Students who feel cell phone usage is addictive.  

 
 
Conclusion 

Society has embraced cell phones and the consequences that cell phones have on our daily life is an important topic.  In this report, the sample provided evidence that the majority of all Flagler College students who find cell phones addictive. In fact, it was estimated that between 87.6% and 95.1% of all Flagler College students find that cell phones are addictive.  Furthermore, it was found that there is statistical evidence that those students who feel it is Important to your social life to always be “connected” via your cell phone are more addicted to their cell phones.  It was estimated that between 18.8% and 20.7% more of all Flagler College students with feelings of having to be connected via cell phone due to social life involvement were addicted by cell phones than all other Flagler College students. This is natural association to me. I feel high usage of cell phones can make me more addicted to the device and that is something that is felt by many people my age. 

 The underlying purpose of cell phones is to help with socialization and connecting people all around the globe faster than ever.  Hence, it is interesting but not surprising that the majority of students feel it is addictive. If there were ways to restrict the time spent on devices maybe we would see declining levels of people admitting that they find cell phones addictive. However our lives are so intertwined with technology and more specifically cell phones that I doubt we will ever see a move towards less time spent on phones.  
 

Data set 1. Raw Data Cell Phones   [Info]
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International Studies Questions

1. Is this a reliable source for information? Why?

Yes, Pew Research Center is a reliable source for information. Pew Research Center have litigable sources when it comes to the data that is being collected for the said project. For example, when it comes to the research conducted for Social Media Use Continues to Rise in Developing Countries but Plateaus Across Developed Ones, those who conducted the research have prestige and sources that help the results.

2. Is the source’s methodology for collecting the data sound? Why or why not?

Yes, the data is sound from the source’s methodology. Pew conducted their surveys for Social Media Use Continues to Rise in Developing Countries but Plateaus Across Developed Ones mainly in the United States in 2018 and in China in 2016. These countries are known for their higher education system and resources to conduct said survey and to obtain all the information.

3. How do the habits of Flagler College students compare to those profiled in this report?

The habits of the Flagler College students who participated in the survey tend to partake more on social media then those who live in developing countries. According to the graphs on Pew Research Center, those who experience the least internet penetration is the continent of Africa. The students who participated in the survey have used the internet for social media and for college purposes making them higher than a whole continent. United States, however, is not in the top three of countries that use the internet in higher rates. The top three are South Korea, Australia and the Netherlands.

4. How do the habitats of Americans compare with other countries?

Even though America is one of the Global Giants of the world, we as a nation compared to the rest of the world do not use as much technology and internet. In developing countries, internet tends to lag when it comes to consumption, but America is not in a higher position in internet penetration. We are, however, have the most people who own a smart phone which causes a raise in prices for the use of internet then other countries.

Result 1: (IMPORTANT AND NOT IMPORTANT) Importance of Social Life on Cell Phone of Students Surveyed in Spring   [Info]
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Result 2: Pie Chart With Data - important and not important vs. addictive cell phones   [Info]
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HTML link:
<A href="https://www.statcrunch.com/5.0/viewreport.php?reportid=87208">PHASE THREE: Cell phones and Flagler College Students in Spring 2019 - Thompson/Wallace/Blonski </A>

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