The Study

We will receive a list of all guys and girls attending NOHS from Mrs. Caso and put it into Minitab. We are using stratified sampling technique by splitting the population into guys and girls. Then we will take a simple random sample of size 80 for both guys and girls using sample from columns in Minitab. Our population of interest is all the students attending North Olmsted High School. It is a simple random sample of size 80 for guys and 80 for girls of the 1527 students at North Olmsted High School.

Our Survey

Circle one: MG MD AH

Male Female

What Cleveland sport team would you prefer to watch?

Cleveland Indians Baseball

Cleveland Browns Football

Cleveland Cavaliers Basketball

Lake Erie Monsters Hockey

Our Data

                 Male Female Total

Indians         9        15          24

Browns        7          6          13

Cavaliers    40       32          72

Monsters     3          3           6

Total            59       56         115

Hypothesis Test

Ho: Gender and Sports Preference have no association

Ha: Gender and Sports Preference have an association

α = 0.05 df = 3

Assumptions: We need all expected cell counts to be greater than or equal to 5. Independently and randomly chosen.

= 2.389177

p-value = .49565

Conclusion: 2 of our expected cell counts were less than 5. Therefore, our chi square test was probably invalid. This could have been contributed to our sample size because of tour response bias.

Minitab Output

Chi-Square Test: Male, Female

Expected counts are printed below observed counts
Chi-Square contributions are printed below expected counts

        Male  Female  Total
    1      9      15     24
       12.31   11.69
       0.891   0.939

    2      7       6     13
        6.67    6.33
       0.016   0.017

    3     40      32     72
       36.94   35.06
       0.254   0.267

    4      3       3      6
        3.08    2.92
       0.002   0.002

Total 59 56 115

Chi-Sq = 2.389, DF = 3, P-Value = 0.496
2 cells with expected counts less than 5.

Revised Hypothesis Test

Ho: There is no difference in Sports Preference among students at North Olmsted High School

Ha: There is a difference in Sports Preference among students at North Olmsted High School

α = 0.05 df = 3

Assumptions: We need all expected cell counts to be greater than or equal to 5. Randomly chosen.

= 92.47826087

p-value ≈ 0

Conclusion: We rejected the null hypothesis at the .05 level of significance because our p-vaule was less than alpha. Therefore, there is sufficient evidence to suggest that there is a difference in sports preference among students at North Olmsted high School in at least one category.

Revised Minitab Output

Chi-Square Goodness-of-Fit Test for Observed Counts in Variable: Observed

                          Test            Contribution
Category  Observed  Proportion  Expected     to Chi-Sq
1               24        0.25     28.75        0.7848
2               13        0.25     28.75        8.6283
3               72        0.25     28.75       65.0630
4                6        0.25     28.75       18.0022

N DF Chi-Sq P-Value
115 3 92.4783 0.000