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Phase Three: Cell Phone Usage at Flagler College

Introduction:

On the First phase of this project as sample of 150 Flagler Students were asked about their Cell Phone Usage habits. Then in the second phase, the 150 students were divided into groups based on whether or not the students believed cell phone usage was Addictive or Non-Addictive. A Bar chart illustrated the data, of the Addictive vs. Non-Addictive.

Result 1: Bar Plot With Data   [Info]

Hypothesis test 1: Majority Test

In the Sample of 150 students, 134 Students reported that they believed that Cell Phone usage was Addictive. 134 out of 150 is 89.33% which is a majority of the sampled students at Flagler college.

Result 2: Pie Chart With Data - Cell Phone - Is it Addictive

Result 2: Pie Chart With Data   [Info]

Hypothesize

Null: Null: Fifty percent of all Flagler College sampled believe that Cell Phone Usage is addictive.

Alternate: More than 50% of Students believe that Cell Phone Usage is Addictive.

Based on the Alternative Hypothesis this a right sided test.

Prepare

1.Random Sample- Possibly not Random, however to proceed we will assume that it is random.

2.Large Sample- Since Np0 =(150)(0.50)=75>=10 and n(1-p0)=(150)(0.50)=75>=10

Both are true so the sample is a large sample.

3. Big Population- Due to 10n= (10)(150)=1500

4. Independence within Sample- Yes, they were independently answered and not influenced in ways that would make it not independent.

Compute

Result 3: One Sample Hypothesis Test

Result 3: result 3   [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
p1341500.893333330.0408248299.6346597<0.0001

Interpret

Due to the P-value being

Confidence Interval #1- Estimating the Population Proportion

The hypothesis test gives evidence that Flagler College students believe that cell phone usage is addictive. Therefore, a confidence interval will be created to see the estimate percentage of Flagler College Students who believe that cell phone usage is addictive. A 90% confidence interval was created as this test was one-tailed and had the significance level of 0.05.

Prepare

1. Random Sample with Independent Observations- Possibly not random. However, to proceed, we will assume that 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)(0.89)=>=10 and n(1-phat)=(150)(1-0.893)=(150)(0.1067)=16.5 >=10, the sample is large

3. Big Population- Due to 10n= (10)(150)=1500

Compute

Result 4: One Sample Confidence Test

Result 4: result 4   [Info]

### One sample proportion summary confidence interval:

p : Proportion of successes
Method: Standard-Wald

95% confidence interval results:
ProportionCountTotalSample Prop.Std. Err.L. LimitU. Limit
p1341500.893333330.025204350.843933720.94273295

Interpret

We are 90% confident that between 85.2% and 93.5% of all Flagler College students believe that cell phone are addictive, which is 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 who are connected to internet on their phones vs. students who believe that cell phone usage is addictive. Of the 89 Addicted Students, 80 were connected to the internet and of the 61 Non-Addicted Students, 54 were connected to the internet. That is, 89.9% (80 students out of 89) of the Addicted Students were connected to the internet and 88.5% (54 students out of 61) of the Non-Addicted Students were connected to the internet. With an approximately 1% difference in these percentages, the sample gives some reason to believe that the population of Addicted Students at Flagler College and the population of Non-Addicted Students at Flagler College differ in their opinion that cell phones are connected.

Result 5: Contingency table (with data) - Addictive Vs. Connected

Result 5: Contingency table (result 5)   [Info]

Rows: Connected
NoYesTotal
No75461
Yes98089
Total16134150

### Chi-Square test:

StatisticDFValueP-value
Chi-square10.0705683680.7905

A hypothesis test will be done to see if this difference is statistical significance 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 significant difference in the proportion of the population of Flagler college students who are connected and believe that cell phone usage is addictive, and Flagler college students who not connected and do not believe that cell phone usage is addictive.

Alternative: There is a significant difference in proportion between Flagler College students who believe that cell phone usage is addictive and that are connected to the internet versus Flagler college students who do not believe cell phone usage is addictive and are not connected.

Prepare:

1. Large Samples- It is found that the sample proportion is,

p-hat = (x1 + x2)/(n1 + n2) = (54+80 )/( 61+89 ) = 134/150 = 0.89333

Sample One (Social Students): Since n1*p-hat = (61)(0.8933) = 54.493 > 10 and

n1*(1 - p-hat) = (61)(1 – 0.8933) = (61)(0.1067) = 6.5087 < 10, sample one is not large.

Sample Two (Unsocial Students): Since n2*p-hat = (89)(0.8933) = 79.5037 > 10 and

n2*(1 - p-hat) = (89)(1 – 0.8933) = (89)(0.1067)= 9.4963 < 10, sample two is not large.

1. Random Sample- They are most likely not however, we will assume that they are.

2. Independent Sample- yes as they students responses were taken in a way that the responses were independent.

3. Independence between samples- Yes there is no relationship between students who believe that cell phone usage is addictive and non-addictive.

Compute

Result 6: Two sample proportion summary hypothesis test

Result 6: result 6   [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 - p2134150161500.786666670.05773502713.625466<0.0001

Interpret:

Since the p – value = 0.0001 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 Social Students at Flagler College and the proportion of the population of Unsocial Students at Flagler College who feel social media is a distraction.

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 addicted students are connected to the internet between the population of Addicted Students at Flagler College and the population of Non-Addicted 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. Large Samples

1. Sample One

1. n1*p-hat1 = (134)(0.773) = 103.582 > 10

2. n1*(1 - p-hat1) = (134)(1-0.773) = 30 > 10

2. Sample Two

1. n1*p-hat1 = (18)(0.773) = 13.914 > 10

2. n1*(1 - p-hat1) = (18)(1-0.773) = 4.086 < 10

2. Random Sample- We will assume that the sampling method was randomized.

3. Big Populations- Flagler College’s student population

4. Independent Sample- Yes, the responses were taken individually, proving that the responses were recorded independently of each other.

Compute

Result 7: Two sample proportion summary confidence interval

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Interpret

This confidence interval is completely positive; this indicates that the population of all Students that use Cell Phones who believe that cell phones are not addictive is less than the percentage of the population of all Addictive Cell Phone use Students who feel their phones are addictive. Thus, I am 95% confident that the percentage of all Cell Phone Addicted Students who feel cell phones are not addictive is between 70.2% and 84.5% greater than the percentage of all Student Cell Phone users who feel cell phones are not 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 find cell phones addictive to their daily life. In fact, it was estimated that between 85.2% and 93.5% 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 that they’re on their cell phones a lot are more addicted to cell phones. It was estimated between 70.2% and 84.5% more of all Flagler College students with feelings of being addicted to their cell phones than all other Flagler College students. This is natural association to me. I feel cell phones can hinder any interaction other than that of my phone. I know I am not alone.

The underlying purpose of cell phones is to help with connecting people and an easier way to expand oneself. Hence, it is interesting that the majority of students feel it is addictive. Maybe a policy of no cell phones for an hour or two, uninterrupted, throughout their day would encourage students to wean off of their phones and possibly be more focussed and motivated to do more throughout their days. It may give students an edge of being more interactive and find interests in something not involving their phones or technology. Although enforcing such a policy that would be difficult, it is something to consider. On the other hand, dividing students into groups randomly each day and having them try new activities is a policy that I will continue to implement to possibly encourage student interaction and none phone enjoyment. Times are always changing but humans are easily indecisive, so hopefully a balance between addictive and non addictive tendencies will be met with the next generations.

Result 7: confidence interval result 7   [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 - p2134150161500.786666670.0356443340.716805060.85652828

Data set 1. Flagler College Students and Cell Phones - Blocher   [Info]