Spatial by TEMPLATED

Sampling

Our populations of interest were all North Olmsted High School freshmen and all North Olmsted High School seniors. First, we needed to obtain a simple random sample of 80 NOHS seniors and 80 NOHS freshmen. To do so, we began with a roster of all NOHS students and eliminated all sophomores and juniors. Then, we used the Calc>Random Data>Sample feature of Minitab to generate two random samples of size 80 without replacement, one of NOHS seniors and one of NOHS freshmen. Then, we used the Data>Sort option to alphabetize both samples. We looked up the schedule of each student in the samples and wrote down an appropriate class to send our surveys to. This anonymous survey contained two questions, the first of which asked what grade the respondent is in, and the second asked whether or not the respondent had attended at least one NOHS sporting event in the past school year.

Significance test

The appropriate statistical test for our data is a two-proportion z-test because our question of interest compares proportions of two different populations.

1) p1-p2 = The difference between the true proportion of freshmen who attended at least one NOHS sporting event in the past school year and seniors who attended at least one NOHS sporting event in the past school year.
2) Ho: p1-p2 = 0
3) Ha: p1-p2<0
4) Alpha: 0.05
5)
6) i. Samples are independent and random
    ii. Sample sizes are sufficiently large:
        n1(p1)=51(.784)=40≥10
        n1(1-P1)=51(.216)=11≥10
        n2(P2)=27(.889)=24≥10
        N2(1-P2)=27(.111)=3<10
    (Though one sample does not meet the size
    requirement, we will proceed with caution.)
7) z = -1.25
8) p-value = 0.105