The table shows the number of votes by fans for contestants on a popular television show. The observed counts are: Contestant A: 120, B: 136, C: 144. Which value represents the degrees of freedom if a goodness-of-fit test is performed?

Rationale

Degrees of freedom in a goodness-of-fit test is calculated as the number of categories minus one.

In this case, there are three contestants (A, B, and C), so the degrees of freedom is calculated as 3 - 1 = 2. This value is essential for determining the critical value in statistical analysis when performing the goodness-of-fit test.

A (1) YOUR ANSWER

This choice suggests that there is only one degree of freedom, which would apply if there were only two categories in the analysis. However, with three contestants, the correct calculation of degrees of freedom is based on the number of categories minus one, which results in a value of 2.

B (2) CORRECT

This is the correct calculation for degrees of freedom in this scenario. The formula for degrees of freedom in a goodness-of-fit test is k - 1, where k is the number of categories. Here, with three contestants, the calculation is 3 - 1 = 2, making this choice accurate.

C (5) YOUR ANSWER

Choosing 5 implies that there are six categories being analyzed, which is incorrect for the given data. The degrees of freedom are derived from the actual number of categories, which is three in this case, leading to a maximum of 2 degrees of freedom after applying the formula.

D (6) YOUR ANSWER

This value suggests that there are seven categories in the analysis, which does not apply here. The degrees of freedom cannot exceed the number of categories minus one, and since there are only three contestants, the maximum possible degrees of freedom is 2.

Conclusion

In a goodness-of-fit test, the degrees of freedom are determined by subtracting one from the number of categories being analyzed. With three contestants, the degrees of freedom for this test is 2, allowing for proper statistical evaluation. Recognizing this is crucial for interpreting test results accurately within the context of the data provided.

The table shows the number of votes by fans for contestants on a popular television show. The observed counts are: Contestant A: 120, B: 136, C: 144. Which value represents the degrees of freedom if a goodness-of-fit test is performed?

Degrees of freedom in a goodness-of-fit test is calculated as the number of categories minus one.

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