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PHASE THREE: Flagler College Students and Censorship Views
Generated Aug 12, 2018 by cmcnulty383

PHASE THREE: Flagler College Students and Censorship Views

Introduction:

In the first phase of this project, the views on Censorship from a sample of 150 Flagler college students was explored. The second phase of this project, the same sample of 150 students were divided into two smaller groups that were referred to as “Desensitized” and “Non-Desensitized” students. The “Desensitized” students define a sample of those Flagler College students who believe that violent television programs do not desensitize people and the “Non-Desensitized” students were those that do believe that violent programs desensitize people. There are 79 Non-Desensitised students, and 71 Desensitized students.

In this phase of this project, the students view as to whether or not the government should control what programs are viewable will be studied.

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 believe that the government should not control viewable programs. A hypothesis test will be run first to find evidence of the majority, and then a confidence interval will be created to estimate the percentage of the population of Flagler College students who believe the government should not control what programs are viewable.

Secondly, the sample results will be used to determine through a two-sample hypothesis test if there is a difference in the proportion of “Desensitized” and the proportion of “Non-Desensitized” students at Flagler College who believe that the government should not decide what programs are viewable. Then a two-sample confidence interval will also be constructed to estimate the difference in the percentage of the population of the “Non-Desensitised” students, and “Desensitized” students who believe that the government should not decide what programs people can view.

Hypothesis Test #1: The Majority Claim

In the sample of 150 students, 144 answered that the government should not decide what programs are viewable. A pie chart of the data is given below. That is the majority being 96%, of the sampled students, believe the government should not control what programs are viewable. These sample results will be used to test the claim that the majority of the population of Flagler College students believe that the government should not decide what programs are viewable at a significance level of 0.5.

<result1>

Hypothesize

Null: Fifty percent of all  Flagler College students believe that the government should not decide what programs are viewable.

Alternate: More than 50% of all Flagler College students believe that the government should not decide what programs are viewable.

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

Prepare

1. Is the sample random? - Most likely not completely random but we will continue with

the belief that it is.

2. Is the sample large? - Since np₀=(150)(0.5)=75≥10 and n(1-p₀) = (150)(1-0.5)=75≥10 are both true, the sample is large.

3. Is there a big population? - Since 10n= (10)(150) = 1500<2500, the population  is big since Flagler College has the approximate population of 2500 students.

4. Is there independence within the sample? - Yes, the student responses were taken in a way that is independent of one another.

Compute

<result2>

Interpret

Since the p-value is (<0.0001) and is, therefore, less than the significance level of 0.5, the null hypothesis is rejected. Therefore, there is sufficient evidence to support the claim that the majority of all Flagler College students believe that the government should not control what programs are viewable.

Confidence Interval #1: Estimating the Population Proportion

The hypothesis test gives sufficient evidence that the majority of all Flagler College students believe that the government should not control what programs are viewable. Therefore, a confidence interval should be created to estimate the percentage of the population who believe that the government should not control what programs are viewable. Since a right-tailed test with a significance level of 0.5 was run, a 90% confidence interval will be created.

Prepare

1. Is the sample random with independent observations? - Again, most likely not

completely random but we will continue with the belief that it is. But yes, the student's responses are independent of one another.

2. Is the sample Large? - Since np̂ = (150)(0.96)= 144 ≥ 10 and n(1-p̂) = (150)(1-0.96) = 6 ≤ 10.

Although this sample does not fit all the standards to be thought of as large, we shall proceed as if it is.

3. Is the population big? -  Since 10n=10(150)=1500<2500, the population is big since Flagler College has 2500 students.

Compute

<result3>

Interpret

We are 90% confident that between 93.37% and 98.63% of all Flagler College students believe that the government should not control what programs are viewable, which is the majority.

Contingency Table #1

A contingency table was created to compare the opinion of the “Desensitized” and “Non-Desensitized” students regarding their belief as to whether or not the government should not control what programs are viewable. Of the 71 “Desensitized” 67 students do not believe that the government should control what programs are viewable, and of the 79 “Non-Desensitized,” 77 students do not believe that the government should control what programs are viewable. That is 94.37% (67/71) of the “Desensitized” students believe that the government should not control what programs are viewable, and 97.47% (77/79) of the “Non-Desensitized” students believe that the government should not control what programs are viewable. With only a 3.1% difference of these two groups, the sample gives some reason to believe that of both the “Desensitized” and “Non-Desensitized” at Flagler College do not differ in their opinion that the government should not control what programs are viewable.

<result4>

Hypothesis Test #2: Difference Between Two Population Proportions

Using the results from the previous contingency graph, a hypothesis test will be used to determine if this difference is statistically significant for the population of students at Flagler College. The test will be run with a 0.5 significance level.

Hypothesis

Null: There is no difference in the proportion of the populations of “Desensitized” students at Flagler College and the proportion of the population of “Non-Desensitized” students at Flagler College who believe that the government should not control what programs are viewable.

Alternate: There is a difference in the proportion of the populations of “Desensitized” students at Flagler College and the proportion of the population of “Non-Desensitized” students at Flagler College who believe that the government should not control what programs are viewable.

Based on the alternate hypothesis, this is a two-tailed test.

Prepare:

1. Is the sample large? - It is found that the pooled sample proportion is

p̂=(x₁+x₂)/(n₁+n₂) = (77+67)/(79+71)= 144/150 = 0.96

Sample One (Desensitized): Since n₁p̂ = (71)(0.96) = 68.16 ≥ 10 and

n₁(1-p̂) = (71)(1-0.96) = 2.84 ≥ 10, ther sample one is large.

Sample Two (Non-Desensitized): Since n₂p̂ = (79)(0.96) = 75.84 ≥ 10 and

n₂(1-p̂) = (79)(1-0.96) = 3.16 ≥ 10, ther sample two is large.

Although these samples do not fit all the standards to be thought of as large, we shall proceed as if they are.

2. Is the sample random? - Most likely not completely random but we will continue under

the belief that it is.

3. Are the samples independent? - Yes, the student responses were taken in a way that is independent of one another.

4. Is there independence within the sample? - Yes, there is no relationship between the “Desensitized” and “Non-Desensitized” students.

Compute

<result5>

Interpret

Since the p-value is (<0.0001) and is, therefore, less than the significance level of 0.5, the null hypothesis is rejected. Therefore, there is sufficient evidence that there is not a significant difference in the proportion of the “Desensitized” and “Non-Desensitized” at Flagler College do not differ in their opinion that the government should not control what programs are viewable.

Confidence Interval #2: The Difference Between the two Population Proportions

The hypothesis test did not give us sufficient evidence that there is a significant difference in the opinion that the government should not control what programs are viewable between the “Desensitized” and “Non-Desensitized” students at Flagler College. Therefore, a confidence interval will be created to estimate this difference and hopefully confirm that the two population proportions are almost equal. Since a two-tailed test was conducted with a significance level of 0.5, a 95% confidence interval will be created.

1. Is the sample random? - Most likely not completely random but we will continue under

the belief that it is.

2.  Is the sample large? - It is found that the pooled sample proportion is

p̂=(x₁+x₂)/(n₁+n₂) = (77+67)/(79+71)= 144/150 = 0.96

Sample One (Desensitized): Since n₁p̂ = (71)(0.96) = 68.16 ≥ 10 and

n₁(1-p̂) = (71)(1-0.96) = 2.84 ≥ 10, ther sample one is large.

Sample Two (Non-Desensitized): Since n₂p̂ = (79)(0.96) = 75.84 ≥ 10 and

n₂(1-p̂) = (79)(1-0.96) = 3.16 ≥ 10, ther sample two is large.

Although these samples do not fit all the standards to be thought of as large, we shall proceed as if they are.

3. Is there a big population? - Since Flagler College has the approximate population of 2500 students we are unsure what the overall percentage of the students are or are not Desensitized and believe that the government should not control what programs are viewable, we will assume 50% are, and 50% are not. Therefore, there are approximately (0.5)(2500) = 1250 students who are Desensitized students and (0.5)(2500) = 1250 students who are Non-Desensitized students in the population.

Population One (Desensitized Students): Since 10n₁= 10(71)=710 <1250 population one is big.

Population Two (Non-Desensitized Students): Since 10n₂= 10(79)=790 < 1250, population two is big

4. Are the samples independent? - Yes, the student responses were taken in a way that is independent of one another.

Compute

<result6>

Interpret

This confidence interval contains zero; this indicates that the percentage of the population of all of the Desensitized Students who feel that the government should not control programs could be the same percentage of the population of all Non-Desensitized Students who feel that the government should not control programs. Thus, I am 95% confident that the percentage of Non-Desensitized Students who feel the government should not control television programs is between 3.3% and 9.5% greater than the percentage of social students who feel that the government should not control television programs.

Conclusion

In this report, the sample provided evidence that the majority of all Flagler College students feel that the government should not control what programs are viewable. In fact, it was estimated that between 93.4% and 98.6% of all Flagler College students agree that the government should not control what programs are viewable. Furthermore, it was estimated that between 3.3% and 9.5% more of all Flagler College students with the feeling that violent programs do not desensitize viewers also believe that the government should not control what programs are viewable. This is logical to me because those who do not have a problem with violent programs stereotypically are those that have negative feelings towards censorship.

Television programs, movies, and video games are all forms of not only entertainment but they also represent the first constitutional right of free speech. Censorship has always been a popular topic because some people believe that the government should intervene, and others believe that if the government did act on censorship laws would be seen as unconstitutional. Perhaps, censorship should remain a constant hot topic, or it could be put away with the implication of being able to choose what media one is exposed to. With parental controls now, what children view can be monitored according to the parents' wishes.

<data1>

Result 1: Government Decides what programs*   [Info]

Result 2: HT1 Gov. Shouldn't Control Programs   [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
p1441500.960.04082482911.267653<0.0001

Result 3: CI1 Gov. Shouldn't Control Programs   [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
p1441500.960.0160.933682340.98631766

Result 4: Contingency table: Should the Government Decide what programs are viewable between Desensitized and   [Info]
Contingency table results:
Rows: Do Violent Programs Desensitize People
Columns: Should Government Decide What Programs
 No Yes Total No 77 2 79 Yes 67 4 71 Total 144 6 150

Chi-Square test:
StatisticDFValueP-value
Chi-square10.937110.333
Warning: over 20% of cells have an expected count less than 5.
Chi-Square suspect.

Result 5: HT2-Sensitised/Descensitised   [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 - p267717779-0.0310215720.032045608-0.968044420.333

Result 6: CI2-Senseitized/Desnsitized   [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 - p267717779-0.0310215720.032575114-0.0948676220.032824477