On the first phase of this project, we began a study of a sample of 150 Flagler College students from the fall semester of 2018 about their opinions on tattoos, and whether or not they had them. In the second phase, the same sample was divided into two smaller samples. The two groups are the sample of Flagler College students who have tattoos and the sample of students who do not have tattoos. Of 150 students sample, 90 students did not have tattoos, while 60 students did. Out of 150 students, 60% do not have tattoos. A bar chart representing the two samples is presented below.
On this phase of the report, attention will be given to whether or not students have tattoos.
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 do not have tattoos. 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 have tattoos.
Second, the sample results will also be used to determine if the parents of the population of all tatted students and the population of all untatted students at Flagler College have a statistically significant chance of having tattoos. 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 tatted and untatted students who have tatted parents.
Hypothesis Test #1  A Claim of Majority
Of the 150 students sampled, 94 did not have tattoos, therefore the majority of students, 62%, had untatted parents. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted. The parents will be referred to as tatted or untatted parents. These sample results will be used to test the claim that the majority of the population of Flagler College students do not have tattoos at a significance level of .05. A pie chart of the data is given below.
Of the 150 students sampled, 90 did not have tattoos, therefore the majority of students, 60%, had no tattoos. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted.
Hypothesize
Null: fifty percent of all Flagler College students did not have tattoos.
Alternate: Less than 50% of all Flagler College students have tattoos.
Prepare
Random Sample Not necessarily because the students that are in statistics class generally are younger students getting their general education classes out of the way. However, for the sake of this assignment, we will assume that it is.
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. Flagler College has a population of approximated 2500 students
Independence within Sample Yes, the responses were taken in ways that prove that they are independent of each other.
Compute
On the first phase of this project, we began a study of a sample of 150 Flagler College students from the fall semester of 2018 about their opinions on tattoos, and whether or not they had them. In the second phase, the same sample was divided into two smaller samples. The two groups are the sample of Flagler College students who have tattoos and the sample of students who do not have tattoos. Of 150 students sample, 90 students did not have tattoos, while 60 students did. Out of 150 students, 60% do not have tattoos. A bar chart representing the two samples is presented below.
On this phase of the report, attention will be given to whether or not students have tattoos.
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 do not have tattoos. 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 have tattoos.
Second, the sample results will also be used to determine if the parents of the population of all tatted students and the population of all untatted students at Flagler College have a statistically significant chance of having tattoos. 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 tatted and untatted students who have tatted parents.
Hypothesis Test #1  A Claim of Majority
Of the 150 students sampled, 94 did not have tattoos, therefore the majority of students, 62%, had untatted parents. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted. The parents will be referred to as tatted or untatted parents. These sample results will be used to test the claim that the majority of the population of Flagler College students do not have tattoos at a significance level of .05. A pie chart of the data is given below.
Result 2: Pie Chart with Data
Of the 150 students sampled, 90 did not have tattoos, therefore the majority of students, 60%, had no tattoos. For the purposes of this project, we will refer to students who have tattoos and tatted, and the students without tattoos and untatted.
Hypothesize
Null: fifty percent of all Flagler College students did not have tattoos.
Alternate: Less than 50% of all Flagler College students have tattoos.
Prepare

Random Sample Not necessarily because the students that are in statistics class generally are younger students getting their general education classes out of the way. However, for the sake of this assignment, we will assume that it is.

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. Flagler College has a population of approximated 2500 students

Independence within Sample Yes, the responses were taken in ways that prove that they are independent of each other.
Compute
p : Proportion of successes
H0 : p = 0.5
HA : p > 0.5
Interpret
Since the pvalue (.9928) is greater than the level of significance of .05, there is not sufficient evidence to reject the null hypothesis.
Results 3: One sample proportion summary hypothesis test Distraction
Confidence Interval #1  Estimating the Population Proportion
Compute
Interpret
We are 90% confident that between 33.4% and 46.6% of all Flagler College students find that their parents do not have tattoos, that attend Flagler College.
Hypothesis Test #2 A Claim of the Difference between two Population Proportions
A contingency table was created to compare the differences between tatted and untatted students based on whether or not their parents were tatted.
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 run at a level of significance of 0.05.
Hypothesize
Null: There is no difference in the proportion of the population of students whose parents do not have tattoos and the proportion of the population of students whose parents do have tattoos.
Alternate: There is a difference in the proportion of the population of students whose parents do not have tattoos and the proportion of the population of students whose parents do have tattoos.
Based on the alternate hypothesis, this is a two tailed test.
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: Tattoo Columns: Parents with Tattoo
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:

Two sample proportion summary confidence interval:p_{1} : proportion of successes for population 1 p_{2} : proportion of successes for population 2 p_{1}  p_{2} : Difference in proportions 95% confidence interval results:

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