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PHASE THREE: VIDEO GAME HABITS OF FLAGLER COLLEGE STUDENTS IN FALL 2018
Generated Dec 7, 2018 by jsaunders363

PHASE THREE: VIDEO GAME HABITS OF FLAGLER COLLEGE STUDENTS IN FALL 2018

Introduction:

On the first phase of this project, the video game habits of a sample of 150 Flagler College students from fall semester 2018 was explored.  In the second phase, this same sample of 150 students was divided into two smaller samples which were referred to as the desensitized Students and the not desensitized Students.  The term “Desensitized Students” defined the sample of those Flagler College students who think video games make them desensitized to violence and the term “Not Desensitized Students” defined the sample of those Flagler College students who do not think video games make them desensitized to violence.  There are 72 Desensitized Students and 78 Not Desensitized Students sampled. A bar chart representing the two samples is presented below.

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On this phase of the report, attention will be given to students’ opinions on whether or not video games are 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 video games 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 feel video games are addictive.

Second, the sample results will also be used to determine if the opinion of the population of all desensitized students and the population of all not desensitized students at Flagler College have a statistically significant difference of opinion regarding the addictivity of video games. 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 desensitized students and not desensitized students on whether or not video games are addictive.

Hypothesis Test #1 – A Claim of Majority

In the sample of 150 students, 128 reported that video games are addictive. That is, the majority, 85.33%, of the students sampled expressed that video games are addictive. These sample results will be used to test the claim that the majority of the population of Flagler College students believe video games are addictive at a level of significance of 0.05  A pie chart of the data is given below.

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Hypothesize

Null: Fifty percent of all Flagler College students believe that video games are addictive

Alternate: More than 50% of all Flagler College students believe that video games are addictive.

Based on the alternate hypothesis, this is a right-sided test.

Prepare

1. Random Sample – Probably not (but we hope it is representative).  However, to proceed, we will assume it is.

2. Large Sample – Since np0 = (150) (0.50) = 75 > 10 and n(1-p0) = (150) (0.50) = 75 > 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.

Compute

Result 3: One sample proportion summary hypothesis test - Addiction

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Interpret

Since the p-value (0.0001) is less than the level of significance of 0.05, we can reject the null hypothesis  Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students feel that video games are addictive.

Confidence Interval #1 – Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students feel that video games are addictive. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that video games are 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 – 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 = (150)(0.8533) = 72 > 10 and n*(1 – phat) = (150)(1 – 0.48) = (150)(0.1467) = 78 > 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

Result 4: One sample proportion summary confidence interval - Addiction

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Interpret

We are 90% confident that between 80.6% and 90.1% of all Flagler College students find that video games are addictive. This is definitely a 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 Desensitized Students and the Not Desensitized Students regarding the if video games are addictive. Of the 72 desensitized Students, 67 felt video games were addictive and of the 78 not desensitized, 61 felt video games are addictive.  That is, 93.1% (67 students out of 72) of the desensitized students felt video games are addictive and 78.2% (61 students out of 78 students) of the not desensitized students felt video games were addictive. With an approximately 15% difference in these percentage, the sample gives some reason to believe that the population of desensitized students at Flagler College and the population of not desensitized Students at Flagler College differ in their opinion on whether video games are addictive.

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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 Desensitized Students at Flagler College and the proportion of the population of Not Desensitized Students at Flagler College who feel video games are addictive.

Alternate: There is a difference in the proportion of the population of Desensitized Students at Flagler College and the proportion of the population of Not Desensitized Students at Flagler College who feel video games are 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) = (61 + 67)/(78 + 72) = 128/150 = 0.8533

Sample One (Social Students): Since n1*p-hat = (78)(0.8533) = 66.5574 > 10 and

n1*(1 - p-hat) = (78)(1 – 0.8533) = (78)(0.1467) = 11.4426 > 10, sample one is large.

Sample Two (Unsocial Students): Since n2*p-hat = (72)(0.8533) = 61.4376 > 10 and

n2*(1 - p-hat) = (72)(1 – 0.8533) = (72)(0.1467) = 10.5624> 10, sample two is large.

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 Desensitized Students and the Not Desensitized Students.

Compute

Result 6: Two sample proportion summary hypothesis test-Desensitized Students VS. Addiction

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Interpret

Since the p – value = 0.0102 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 Desensitized Students at Flagler College and the proportion of the population of Not Desensitized Students at Flagler College who feel video games are 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 video games are addictive between the population of Desensitized Students at Flagler College and the population of Not Desensitized 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 (Desensitized Students): Since n1*p-hat1 = (78)(.782) =60.996 > 10 and

n1*(1 - p-hat1) = (78)(1 – 0.782) = (78)(0.218) =17 > 10, sample one is large.

Sample Two (Unsocial Students): Since n2*p-hat2 = (72)(0.931) = 67.032 > 10 but

n2*(1 - p-hat2) = (72)(1 – 0.931) = (72)(0.069) = 4.968 < 10, sample two is not large, but to proceed we will assume it is.

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 by desensitizing through video games, we will assume 50% are and 50% are 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)(78) C= 780 < 1250, population one is big.

Population Two (Unsocial Students): Since 10n2 = (10)(72) = 720 < 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.

Compute

Result 7: Two sample proportion summary confidence interval - Desensitized Students VS. Addiction

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Interpret

This confidence interval is completely negative; this indicates that the percentage of the population of all Desensitized Students who feel video games are addictive is less than the percentage of the population of all Not Desensitized Students who feel video games are addictive.  Thus, I am 95% confident that the percentage of all Desensitized Students who feel video games are addictive is between 3.97% and 25.7% greater than the percentage of all Desensitized Students who feel Video games are addictive.

Conclusion

In our society, video games are a widely enjoyed form of entertainment. As video games continue to develop, it is important to examine the effects that video games have one people and society as a whole. In this report, the sample provided evidence that the majority of all Flagler College students find video games to be addictive. In fact, it was estimated that between 80.6% and 90.1% of all Flagler College students find that video games are addictive. Furthermore, it was found that there is statistical evidence that those students who feel violence in video games causes desensitization to violence feel that video games are addictive.  It was estimated that approximately 15% more of all Flagler College students who feel that violence in video games causes desensitization to violence felt that video games were addictive more than all other Flagler College students. This makes sense because it would seem that people who already have a negative association with videogames would be more likely to think that they were addictive, another negative association.

The purpose of video games is to be a form of entertainment and an escape from the troubles of reality. Thus, it is makes sense that the majority of students feel that they can be addictive.  Maybe if people took the initiative to limit their video game play time to only an hour or two daily, people could find more of a balance between playing video games and participating in their daily lives. Likewise, I believe parents should monitor what video games their children play and determine how much play time a day is healthy so that children can learn to develop healthy video game habits. Hopefully in the future, people can find more of a balance between their daily lives and their virtual lives.

Result 1: Students Desensitized and Students Not Desensitized   [Info]

Result 2: Pie Chart With Data   [Info]

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
p1281500.853333330.0408248298.6548638<0.0001

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
p1281500.853333330.028885470.805820960.9008457

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

Rows: Violence
NoYesTotal
No176178
Yes56772
Total22128150

### Chi-Square test:

StatisticDFValueP-value
Chi-square16.59726020.0102

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 - p261786772-0.148504270.057817212-2.56851320.0102

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 - p261786772-0.148504270.055522477-0.25732633-0.039682218