To obtain our sample, we used Minitab to randomly generate thirty teachers and one hundred students from North Olmsted High School.  The students ranged from ninth to twelfth grade, and the sample included all staff members.  Then, we created a survey that asked, “Wearing thin strapped tank tops in school is appropriate” and “Should the school dress code dealing with tank tops (“Tank tops, cutoff shirts, or any garment, which reveals undergarments, are not appropriate.”) be changed?”  The options of answers for the first question were strongly agree, agree, no opinion, disagree, and strongly disagree.  The options of answers for the second question were yes, no, and no opinion.  Out of the 130 surveys sent out, 91 were returned.

  
Please circle one of the following: 
1. Wearing thin strapped tank tops in school is appropriate.
 Strongly Agree Agree No opinion Disagree Strongly Disagree

2. Should the school dress code dealing with tank tops (“Tank tops, cutoff shirts, or any garment, where reveals undergarments, are not appropriate.”) be changed?
Yes No No opinion

 

        In our study, we chose to run two different significance tests. In the first test, we chose to run a chi-squared test for independence because we wanted to know if there was an association between a person’s opinion on the appropriateness of then strapped tank tops in school and their opinion on changing the dress code.

Ho: There is no association between a person’s opinion on the appropriateness of then strapped tank tops in school and their opinion on changing the dress code.

Ha: There is an association.

Significance level: α= 0.05

Assumptions: The samples are simple random samples. However, we have to assume that the population is normal because there are two expected cell counts that are less than five.

Test statistic:

54.865 at 4 degrees of freedom

P-value= 0

        In our second test, we decided to run a difference of proportions test in order to know if the true proportion of those who agree with the appropriateness of thin strapped tank tops in school is greater than the proportion of those who disagree.

π₁: The true proportion of people who agreed that wearing thin strapped tank tops in school is appropriate.

π₂: The true proportion of people who disagreed that wearing thin strapped tank tops in school is appropriate.

Ho: π₁-π₂=0

Ha: π₁-π₂ > 0

Significance level: α= 0.05

Assumptions: The samples are simple random samples. n₁p₁ = 21.27 >10, n₁(1-p₁) = 22.73 > 10, n₂p₂= 9.24 <10, n₂(1-p₂)= 19.76 >10

Test statistic: