In the first phase of our project, we explored 150 Flagler College Statistic students opinions regarding Marijuana use. In the second phase of our project, we divided our sample of 150 students into two groups those who think marijuana is equivalent to tobacco, and those who do not. We will refer to these students as equal students and unequal students. There are 110 equal students and 40 unequal students.
On this phase of the report, attention will be given to students’ opinions if Marijuana is equivalent to alcohol.
First, our statistical analysis will determine if the sample results reflect that the majority of students at Flagler College believe marijuana is equivalent to alcohol. We will first run a hypothesis test that will allow us to find where the majority of students opinions lie. We will then create a confidence interval in order to estimate the percentage of all students at Flagler College who believe marijuana is equivalent to alcohol.
We will then use our sample results in order to determine if the opinions of of all Equal Students and Unequal Students at Flagler College have differing opinions regarding if marijuana is different from alcohol. We will then run a hypothesis test and confidence interval in order to find statistical differences.
Hypothesize:
Null: 50% of Flagler College Statistics Students surveyed think that Marijuana is not Equivalent to alcohol.
Alternate: More than 50% of the Students surveyed think Marijuana is not the same as alcohol.
Check to Meet Conditions:

Random Sample: Assumed to be random.

Large Sample Equation:
np0 = (150) (0.50) = 75 > 10 and n(1p0) = (150) (0.50) = 75 > 10 which means that both true statements have a large sample
3. Big Population Equation:
Since the formula is 10n = (10)(150) = 1500 < 2500, means the population is big. Flagler College has roughly around 2,500 students.
4. Independence within Sample: This statement for each student was independent because it relied on their each personal opinion.
Interpret:
Since the Pvalue (.9995) is greater than the significance level of .05, we have enough evidence to fail to reject the null hypothesis. This being said, there is not sufficient evidence to support the claim that the majority of Flagler College Students believe that marijuana is equivalent to alcohol.
Confidence Interval #1 Estimating the Population Proportion
The hypothesis test gives sufficient evidence that the majority of all Flagler College students do not feel that marijuana is equal to alcohol. Therefore, a confidence interval will be created to estimate the percent of the population of all Flagler College students who believe that marijuana is equal to alcohol. In order to do so, we will create a 90% confidence interval because we had one tail area.
Prepare:

Random Sample with Independent Observations: Sample is assumed to be Random and date was collected in a manner that ensures independent observations.

Large Samples: Large Sample Equation:
np0 = (150) (0.50) = 75 > 10 and n(1p0) = (150) (0.55) = 83 > 10 which means that both true statements have a large sample

Big Population: Since the formula is 10n = (10)(150) = 1500 < 2500, means the population is big. Flagler College has roughly around 2,500 students.
Interpret:
We are 90% confident that between 30.2% and 43.1% of all Flagler College students think that marijuana is equivalent to alcohol. Since both numbers fall within the interval are below 50%, we are able to say that a majority of Flagler College students do not think alcohol is equal to marijuana.
Hypothesis Test #2:
A contingency table was created in phase 2 of our project in order to compare the opinions of the Equal Students and Unequal Students regarding if they believe marijuana to be equal to alcohol. Of the 40 Equal Students, 15also believed that marijuana is equal to alcohol. In addition, of the 110 Unequal Students, 70 felt that marijuana is not equal to alcohol. In other words, 37.5% (15 students out of 40) of the Equal Students felt that marijuana is equal to alcohol and 63.6% (70 students out of the 110 students) of the Unequal Students felt that marijuana is equal to alcohol. With an approximate difference of 26.1%, the sample gives us reason to believe that the population of Equal Students at Flagler College and the population of Unequal Students at Flagler College differ in their opinion that marijuana is equal to alcohol.
Contingency Table
Rows: Sample(Sample(Equal to Tobacco))
Columns: Sample(Equal to Alcohol)
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 Equal Students at Flagler College and Unequal Students at Flagler College who think that marijuana is the same as alcohol.
Alternate: There is a difference in the proportion of the population of Equal Students at Flagler College and Unequal Students at Flagler College who think that marijuana is the same as alcohol.
Based off of the alternative hypothesis, this is a twotailed test.
Prepare:

Large Samples

Random Samples: Assumed to be random.

Independent Samples: Yes, the student responses were recorded in a manner that ensures the responses are independent of each other.

Independence between Samples: Yes, there is no relationship between Equal Students and Unequal Students.
Interpret
Since the Pvalue of .8984 is greater than the significance level of .05, we fail to reject the null hypothesis. Therefore, there is not sufficient evidence that there exists a difference in the proportion of the population of Equal Students at Flagler College and the proportion of the population of Unequal Students at Flagler College who believe marijuana is equal to alcohol.
Confidence Interval #2 Estimate the Difference between two Population Proportions
The hypothesis test we ran provides us with sufficient evidence to support that there is a significant difference in the opinion that marijuana is equal to alcohol between the population of the Equal Students at Flagler College and the population of Unequal Students at Flagler College. Therefore, we will perform a confidence interval with 95% confidence due to the fact that it is a twotailed test with a significance level of .05. The confidence interval will either confirm or deny the two population proportions are not equal.
Prepare

Random Samples with Independent Observations Samples are assumed to be random and surveys were taking in a manner in which they are independent of one another.

Large Samples
Sample One (Equal Students): Since n1*phat1= (40)(.733)= 29.32 > 10
n1*1phat1= (40)(.267)= 10.68 > 10 Sample One is large.
Sample Two (Unequal Students): Since n2*phat2= (110)(.267)= 29.37 > 10
n2*1phat2= (110)(.733)= 80.63 > 10 Sample Two is large.

Big Populations Assuming 50% of students are Equal and 50% are not, we can conclude that (.50)(2500) = 1250 Students who are equal and 1250 Unequal Students.
Population One (Equal Students): Since 10n1= (10)(40)= 400 < 1250. Population One is big.
Population Two (Unequal Students): Since 10n2= (10)(110)= 1100 < 1250. Population Two is big.

Independent Samples This statement for each student was independent because it relied on their each personal opinion.
Interpret
Since this confidence interval contains 0, we can conclude that the percentage of the population of Equal Students who feel marijuana is equal to alcohol could be equal to the population of Unequal Students who feel marijuana is equal to alcohol. Therefore, I am 95% confident that the percentage of all Unequal Students who believe marijuana is equal to alcohol is equal to the percentage of all Equal Students who think marijuana is equal to alcohol.
Conclusion
In this report, our sample supported the notion that a majority of Flagler College students believe marijuana to not be equal to alcohol. In particular, we found that approximately between 30.2% and 43.1% of all Flagler College Students believe that marijuana is not equal to alcohol. Since both numbers in the interval do not include 50%, we can conclude that the majority of Students do not think marijuana and alcohol are equal. In addition, we also found statistical evidence to support that Unequal students, or those who believe marijuana and tobacco are different, were more inclined to say that marijuana is different from alcohol as well. This makes sense due to the fact that, those who find tobacco and marijuana to be different would be more likely to also see the difference between marijuana and alcohol considering alcohol and marijuana are completely different substances.
One sample proportion summary hypothesis test:p : Proportion of successes H_{0} : p = 0.5 H_{A} : p > 0.5 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:

Contingency table results:Rows: Sample(Equal to Alcohol) Columns: Sample(Equal to Tobacco)
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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