Introduction:
In the first phase of the project, a sample of 150 Flagler College students in the 2018 Fall Semester of the MAT223 class were surveyed on their views on cell phone usage. In the second phase of the project the same sample of 150 Flagler students was divided into two groups: the students who believed that cell phones are important to stay connected (connected students), and the students who believed that cell phones are not important when trying to stay connected (disconnected students). In phase three we use the same categorized group of students and use statistical inferences to indicate that the majority of Flagler students do NOT think that posting daily is important when trying to stay connected. A bar chart is represented below.
First, 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 do NOT think that posting daily is important when trying to stay connected.
Second, the sample results will also be used to determine if the opinion of the population of all connected students and the population of all disconnected students at Flagler College have a statistically significant difference of opinion regarding whether or not cell phones are important when trying to stay connected. 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 connected and disconnected students who do NOT think that posting daily is important when trying to stay connected.
Hypothesis Test One: A Claim of Majority
In the sample of 150 students, 138 of the students reported that they do NOT think that posting daily is important when trying to stay connected. That is the majority, 92%, of the students sampled expressed that they do NOT think that posting daily is important when trying to stay connected. These sample results will be used to test the claim that the majority of the population of Flagler college students do NOT think that posting daily is important at a significance level of .05, a pie chart is given below.
Hypothesize:
Null Hypothesis: 50% of all Flagler college students do NOT think that posting daily is important when trying to stay connected.
Alternate Hypothesis: More than 50% of all Flagler college students do NOT think that posting daily is important when trying to stay connected.
Based on the alternate hypothesis, this is a rightsided test.
Prepare:

Random Sample: Assumed True

Large Sample: Since np0 = (150) (0.50) = 75 > 10 and n(1p0) = (150) (0.50) = 75 > 10 are both true statements, the sample is large.

Big Population: Since 10n = (10)(150) = 1500 < 2500, the population is big. Recall, Flagler College has a population of appropriately 2500 students.

Independent Sample: Yes, the student responses were taken in such a way that their responses were independent of each other.
Compute:
Do NOT Think that Posting Daily is Important One Sample Proportion Summary Hypothesis Test:
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5
Hypothesis Test One Results:
Proportion 
Count 
Total 
Sample Prop. 
Std. Err. 
ZStat 
Pvalue 
p 
138 
150 
0.92 
0.040824829 
10.287857 
<0.0001 
Interpret:
Since the pvalue (
Confidence Interval #1 Estimating the Population Proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College students do NOT think that posting daily is important when trying to stay connected. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who think that posting daily is NOT important when trying to stay connected. Since a one tailed test with a level of significance of 0.05 was run, a 90% confidence interval will be created.
Prepare:

Random Sample: Assumed True
Furthermore, yes, the student responses were taken in such a way that their responses were independent of each other.

Large Sample – Since n*phat = (150)(0.92) = 138 > 10 and n*(1 – phat) = (150)(1 – 0.92) = (150)(0.08) = 12 > 10, the sample is large.

Big Population – Since 10n = (10)(150) = 1500 < 2500, the population is big. Flagler College has a population of appropriately 2500 students, so the big population standard is met.
Compute:
Do NOT Think that Posting Daily is Important One Sample Proportion Summary Confidence Interval:
p : Proportion of successes
Method: StandardWald
90% confidence interval results:
Proportion 
Count 
Total 
Sample Prop. 
Std. Err. 
L. Limit 
U. Limit 
p 
138 
150 
0.92 
0.022150997 
0.88356485 
0.95643515 
Interpret:
We are 90% confident that between 88.4% and 95.6% of all Flagler College students do NOT think that posting daily is important in order to stay connected. This is certainly 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 responses of the Connected Students and the Disconnected Students whether or not they had parental controls on their phones. Of the 70 Disconnected Students, 58 of them claimed that they did NOT have parental controls on their phones. Of the 80 Connected Students, 60 of them claimed that they did NOT have parental controls on their phones. That is, 82.9% of the Disconnected Students did NOT have parental controls on their phones and 75% of the Connected Students did NOT have parental controls on their phones. With an approximately 7.9% difference in these percentage, the sample gives some reason to believe that the population of Disconnected and Connected students at Flagler College differ in their responses about whether or not they had parental controls on their phones. The majority of the Disconnected and Connected Students at Flagler College did NOT have parental controls on their phones.
Contingency Table Results:
Rows: Connected
Columns: Parental Controls
No 
Yes 
Total 

No 
58 
12 
70 
Yes 
60 
20 
80 
Total 
118 
32 
150 
ChiSquare test:
Statistic 
DF 
Value 
Pvalue 
Chisquare 
1 
1.3733354 
0.2412 
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 Disconnected Students at Flagler College and the population proportion of Connected Students at Flagler College who did NOT have parental controls on their phones.
Alternate: There is a difference in the proportion of the population of Disconnected Students at Flagler College and the proportion of the population of Connected Students at Flagler College who did NOT have parental controls on their phones.
Based on the alternate hypothesis this is a two tailed test.
Prepare:

Large Samples: It is found that the pooled sample proportion is,

phat = (x1 + x2)/(n1 + n2) = (12 + 20)/(70 + 80) = 32/150 = 0.21

Sample One (Connected Students): Since n1*phat = (70)(0.21) = 14.7 > 10 and,

n1*(1  phat) = (70)(1 – 0.21) = (70)(0.79) = 55.3 > 10, sample one is large.

Sample Two (Disconnected Students): Since n2*phat = (80)(0.21) = 16.8 > 10 and,

n2*(1  phat) = (80)(1 – 0.21) = (81)(0.79) = 63.2 > 10, sample two is large.


Random Samples: Again, probably not (but we hope they are representative). However, to proceed, we will assume that they are.

Independent Samples: Yes, the student responses were taken in such a way that their responses were independent of each other.

Independence between Samples: Yes, there is no relationship between the Disconnected and Connected Students.
Compute:
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. 
ZStat 
Pvalue 
p1  p2 
60 
80 
58 
70 
0.078571429 
0.067046537 
1.1718939 
0.2412 
Interpret:
Since the pvalue = .2412 is greater than the level of significance of 0.05, the null hypothesis will fail to be rejected. Therefore, there is not sufficient evidence that there exists a difference in the proportion of the population of Connected Students at Flagler College and the proportion of the population of the Disconnected Students at Flagler College who did NOT have parental controls.
Confidence Interval #2  Estimate the Difference between Two Population Proportions
The hypothesis test gave us sufficient evidence that there is NOT a significant difference of responses between the population of Connected Students at Flagler College and the population of Disconnected Students at Flagler College Therefore, a confidence interval is not necessary.
Conclusion:
Cell phones play a major role in today’s society, and thus is an important topic. In this report, the sample provided evidence that the majority of all Flagler College students do NOT think posting daily is important in order to stay connected. In fact, it was estimated that between 88.4% and 95.6% of all Flagler College students do NOT think that posting daily is important in order to stay connected. Furthermore, it was found that there is statistical evidence that those students who feel cell phones are important to stay connected are no more or less likely to have had parental controls on their phones. Therefore, no further confidence interval could be conducted, as there was no difference between the groups.
Today, cell phones have a wide array of purposes, they assist in socialization, the availability of information, and of course communication, among other uses. There are actually so many uses, that some parents feel the need to put parental controls on their children's’ cell phones. The good news is that the factor of parental controls creates no differences in the responses of students to whether they think that cell phones are important to stay connected. With that being said, since parental controls are not impactful on if students feel as though cell phones are important, they can be eliminated as a contributing factor of determination.
One sample proportion summary hypothesis test:p : Proportion of successes H_{0} : p = 0.5 H_{A} : p > 0.5 Hypothesis test results:

One sample proportion summary confidence interval:p : Proportion of successes Method: StandardWald 90% confidence interval results:

Contingency table results:Rows: Connected Columns: Parental Controls
ChiSquare test:

Two sample proportion summary hypothesis test:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions H_{0} : p_{1}  p_{2} = 0 H_{A} : p_{1}  p_{2} ≠ 0 Hypothesis test results:

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