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Answer:
It can be concluded that participation in sports is dependent on grade level.
Step-by-step explanation:
In this case a Chi-square independence test for the data is to be performed at <em>α </em>= 0.01.
The hypothesis can be defined as follows:
H₀: The participation in sports is independent of grade level.
<em>Hₐ</em>: The participation in sports is dependent of grade level.
The data provided is:
Freshmen Sophomores Juniors Seniors
Yes 75 88 55 42
No 30 28 38 40
The formula to compute the expected frequencies is:
The Chi-square statistic is:
Consider the Excel file attached below.
The value of Chi-square statistic is 16.244.
The degrees of freedom of the test are:
Compute the <em>p</em>-value of the test as follows:
*Use a Chi-square table.
<em>p</em>-value = 0.001 < <em>α</em> = 0.01
The null hypothesis will be rejected at 1% level of significance.
Thus, it can be concluded that participation in sports is dependent on grade level.
