Sampling

For our study we used a sample of students from the population of students from North Olmsted High School. Using the program of Minitab we randomly generated a list of 200 students from the population of North Olmsted High School. After sorting the list alphabetically we went to the guidance office and looked through schedules to find the best period and teacher to contact each student in our sample. We then put the information we gathered on post it notes and put the post it notes on anonymous surveys to be delivered to the teachers. Mrs. Caso then distributed the surveys to the appropriate teacher’s mailboxes to be delivered to the students in our sample. From the returned surveys our sample size was cut down to 155. Here is a copy of the survey that was distributed to our sample:

Anonymous Survey

What is your favorite band or musical artist?         

 ______________________________

What is your cumulative GPA?                              

 ______________________________

 

Significance Test

For our study, we used a chi-square test for indepence. We chose this test because our objective was to determine if there was an association between two categorical values; music taste and gpa. Even though GPA is a numerical value, we sorted into categories of 2, 3, and 4. The categories are as follows:

 0-2.999 = 2

3.000-3.999 = 3

4.000-5.000 = 4

Null Hypothesis: H0 - Taste in music and GPA are independent

Alternative Hypothesis: Ha - Taste in music and GPA are not independent.

Significance level: α = 0.05

Test Statistic:

Assumptions:  1. The observed counts are from a random sample

 2. The sample size was NOT sufficiently large. Out of our 21 cells, 8 of the expected cell counts were less than 5. This was after we already combined categories to increase the cell counts and we feel that making any more combinations would make any findings inaccurate.

Rows: Genre                Columns: GPA Categories
                                    2                 3                 4                      All

Alternative Rock           7                10                5                      22
                                    8.090         10.219         3.690               22.000

Country                        6                 7                 4                      17
                                    6.252          7.897          2.852               17.000

Pop                              8                 22               2                      32
                                   11.768         14.865        5.368               32.000

Punk Indie                   3                  4                4                      11
                                    4.045           5.110         1.845               11.000

Rap                             23                18               7                      48
                                   17.652         22.297        8.052               48.000

Rock                            7                  8                 1                      16
                                   5.884           7.432          2.684               16.000

Slow Music                  3                  3                 3                       9
                                   3.310           4.181          1.510                9.000

All                                57               72                26                    155
                                   57.000         72.000        26.000             155.000

Pearson Chi-Square = 16.694, DF = 12, P-Value = 0.161
Likelihood Ratio Chi-Square = 16.352, DF = 12, P-Value = 0.176

Conclusion: We fail to reject the null hypothesis at the 0.05 level of significance sicne the P-Value is greater than alpha. Therefore, we have insufficient evidence to say that there is an association between taste in music and GPA.