The Study

Our Sampling Method

We used Minitab to randomly generate the names of 60 faculty members and also 30 numbers that corresponded to the specific parking permit number each student with a parking pass has. We were fortunate enough to get a list of every student in North Olmsted High School that owns a parking pass, which also had the model year of their car written on it. From there, we realized that there was a number (1 through 297) corresponding to each students’ name. We randomly generated 30 numbers between 1 and 297 and matched those numbers to people with parking passes, and then we recorded the age of their cars. After receiving the faculty surveys back and matching the Minitab generated numbers to names of students with parking passes, we had our data. We had a total of 44 faculty surveys returned to us with 4 being invalid responses. We also used Minitab to generate 30 numbers (between 1 and 40) to use for the teacher’s portion, and then matched those numbers to the corresponding number of the teacher survey. So we used a total of 30 teacher responses and 30 student responses. We then ran a 2 sample t-test to determine if teachers had newer cars than students, on average.

This is the survey question we sent out to 60 North Olmsted High School teachers:

What is the model year of the car you drive to school?

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1) u1=the true mean model year of students' cars 
    u2=the true mean model year of teachers' cars
2) H0: u1=u2
3) Ha: u1<u2
4) alpha=0.05
5) Assumptions: Our data is random and independently selected. Our sample size is greater than 30, therefore the Central Limit Theorem applies and our data is normally distributed.
6) Two Sample T-Test:
7) p-value=0
8) test statistic= -4.35  degrees of freedom=n-2=58
9) Conclusion: We can reject the null hypothesis at any reasonable level of significance because our p-value is less than alpha. Therefore, there is sufficient evidence to suggest that the true mean model year of teacher's cars is greater than the true mean model year of students' cars.