A high school runs a survey asking students if they participate in sports. The results are found below. Run an independence test for the data at α=0.01. Freshmen Sophomores Juniors Seniors Yes 75 88 55 42 No 30 28 38 40 Can it be concluded that participation in sports is dependent on grade level?

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 α = 0.01.

The hypothesis can be defined as follows:

H₀: The participation in sports is independent of grade level.

Hₐ: 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 p-value of the test as follows:

*Use a Chi-square table.

p-value = 0.001 < α = 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.

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step-by-step explanation:

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