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Owner: otisher469
Created: Dec 6, 2018
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Stat Project: Phase 3

Introduction:

In the first phase of this project, the video game habits of a sample of 150 Flagler College students from Fall semester 2018 were surveyed. In the second phase of this project, the same sample, of 150 Flagler Students, will be divided into two smaller groups. The two samples are the sample of who think that video games cause violence and the sample of Flagler Students who do not think that video games cause violence. The term “Yes” defines the sample of Flagler College students who think that video games desensitize players from violence and the term “No” defines the sample of Flagler College students who do not think that video games desensitize players from violence. There are 78 Yes students sampled and 72 No students sampled.  The bar chart below illustrates this.

Result 1: Result 1: Yes or No to Desensitizing Violence   [Info]

On this phase of the report, attention will be given to students’ opinions that video games cause violence.

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 it is safe to play video games with strangers. 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 that it is safe to play video games with strangers.

Second, the sample results will also be used to determine if the opinion of the population of all “Yes” Students and the population of all “No” Students at Flagler College have a statistically significant difference of opinion regarding that it is safe to play video games with strangers.  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 “Yes” Students and “No” Students who feel that it is not safe to play video games with strangers.

Hypothesis Test #1: Claim of Majority

In the sample of 150 students, 78 students reported that it is safe to play video games with strangers. That is, the majority, 52%, of the students sampled feel that it is safe to play video games with strangers. These sample results will be used to test the claim that the majority of the population of Flagler College students feel that it is safe to play video games with strangers is at a level of significance of 0.05  A pie chart of the data is given below.

Result 2: Safe To Play With Strangers Fall 2018   [Info]

Hypothesize

Null: Fifty percent of all Flagler College students feel that it is safe to play with strangers.

Alternate: More than 50% of all Flagler College students feel that it is safe to play with strangers.

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 continue it we are under assumption that 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 a specific way therefore, making them independent of each other.

Compute

Result 3: 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
p1061500.706666670.0408248295.0622788<0.0001

Interpret

Since the p-value (safe to play video games with strangers.

Confidence Interval #1 – Estimating the Population Proportion

The hypothesis test does not give sufficient evidence that the majority of all Flagler College students feel that it is safe to play video games with strangers.  Therefore, a confidence interval will be created to further estimate the percent of the population of all Flagler College students that it is safe to play video games with strangers. 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 –Yes, the student responses were taken in a specific way therefore, making them independent of each other.

2. Large Sample – Since n*phat = (150)(0.0.71) = 107 > 10 and n*(1 – phat) = (150)(1 – 0.71) = 149 (150)(0.29) = 44  > 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, which is large.

Result 4: 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
p1061500.706666670.0371742640.645520440.76781289

Interpret

We are 90% confident that between 64.5% and 76.7% of all Flagler College students feel that vit is safe to play with strangers.

Hypothesis Test #2 – A Claim of the Difference between two Population Proportions

A contingency table was created to compare the opinions of the students think that video games desensitize players from violence and if it is safe to play with strangers. Of the 72 students that said video games caused violence, 59 said yes that it caused violence and of the 78 student that said that it is safe to play with strangers, 47 said yes. 81.9% (59 students out of 72) of the students that said video games desensitize players from violence and 60.3% (47 students out of the 78) of the students said yes to video games being safe to play with strangers. There is a 22% difference in these percentage, the sample gives some reason to believe that the population of students that said yes to video games causing violence at Flagler College and the population of students that said yes to it being safe to play video games with strangers.

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.

Result 5: Result 5: Contingency Table   [Info]

### Contingency table results:

Rows: Video Games Desensitize Violence
Columns: Safe to Play with Strangers
NoYesTotal
No135972
Yes314778
Total44106150

### Chi-Square test:

StatisticDFValueP-value
Chi-square18.49572010.0036

Hypothesize

Null: There is no difference in the proportion of the population of the students that said yes to video games causing violence at Flagler College and the proportion of the population of students that said yes to it being safe to play video games with strangers.

Alternate: There is a difference in the proportion of the population of the students that said yes to video games desensitize players from violence  at Flagler College and the proportion of the population of students that said yes to it being safe to play videogames with strangers.

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) = (59 + 47)/(72 + 78) = 106/150 = 0.7067

Sample One (yes to violence): Since n1*p-hat = (72)(0.7067) = 50.9 > 10 and

n1*(1 - p-hat) = (72)(1 – 0.7067) = (72)(0.2933) = 21.2 > 10, sample one is large.

Sample Two (yes to dangerous to play video games with strangers): Since n2*p-hat = (78)(0.7067) = 55.1 > 10 and

n2*(1 - p-hat) = (78)(1 – 0.7067) = (78)(0.2933) = 22.9 > 10, sample two is large.

2. Random Samples – We will assume they are representative.

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 students that believe video games desensitize players from violence and if it is safe to play with strangers.

Compute:

Result 6: Two sample proportion summary hypothesis test- HT #2   [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 - p2597247780.216880340.0744080792.91474190.0036

Interpret

Since the p – value = 0.0036 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 students that say yes to video games desensitize players from violence at Flagler College and the proportion of the population of students that said yes to danger playing video games with strangers at Flagler College.

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 students say yes to video games desensitizing players from violence at Flagler College and the population of students saying yes to it being dangerous playing video games with strangers 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 90% confidence interval will be created.

Prepare

1. Random Samples with Independent Observations – Yes, the students responses were independent of one another.

2. Large Samples

Sample One (video games desensitize players from violence ): Since n1*p-hat1 = (72)(0.819) = 59 > 10 and

n1*(1 - p-hat1) = (72)(1 – 0.819) = (72)(0.181) = 13 > 10, sample one is large.

Sample Two (yes to danger playing video games with strangers): Since n2*p-hat2 = (78)(0.603) = 47 > 10 and

n2*(1 - p-hat2) = (78)(1 – 0.181) = (78)(0.819) = 64 > 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 that say video games desensitize players from violence , we will assume 50% say yes and 50% say no.  Hence, there are approximately (0.50)(2500) = 1250 students who said yes to video games desensitize players from violence and (0.50)(2500) = 1250 students who say yes to danger playing video games with strangers in the population.

Population One (video games desensitize players from violence ): Since 10n1 = (10)(72) = 720 < 1250, population one is big.

Population Two (yes to danger playing video games with strangers): Since 10n2 = (10)(78) = 780 < 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- CI #2   [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

90% confidence interval results:
DifferenceCount1Total1Count2Total2Sample Diff.Std. Err.L. LimitU. Limit
p1 - p2597247780.216880340.0715904890.0991244660.33463622

Interpret:

We are 90% confident that between 9.9% and 33.5% of all Flagler College students feel that video games do not desensitize players from violence.

Conclusion:

Many studies have been done to test whether or not video games desensitize players from violence. in this report, the sample of 150 Flagler College students provided evidence that the majority feel that video games it is safe to play video games with strangers. It was calculated that between 64.5% and 76.7% of Flagler College students feel that it is safe to play video games with strangers. However, it was tested that students feel that video games do not desensitize players from violence. It was calculated that between 9.9% and 33.5% of all Flagler College students feel that video games do not desensitize players from violence. This is a natural correlation as video games desensitizing players from violence is a personal opinion and that the students believe it is safe to play video game with strangers.

Data set 1. Flagler College Students and Video Games - Loveday   [Info]