A researcher collected data on the preferences for the location of a major sporting event. The observed counts are: Location A: 310, B: 340, C: 350. Which value represents the degrees of freedom if a goodness-of-fit test is performed?

Rationale

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

In this case, there are three locations (A, B, and C), so the degrees of freedom is computed as 3 - 1, which equals 2. This value is essential for determining the critical value from the chi-square distribution during hypothesis testing.

A (1) YOUR ANSWER

A degrees of freedom value of 1 would imply there is only one category minus one, which does not reflect the three categories in this scenario. This value does not account for the multiple observed counts and is therefore incorrect for this goodness-of-fit test.

B (2) CORRECT

Correctly calculated as the number of categories minus one (3 - 1 = 2), this value represents the degrees of freedom needed for the chi-square test. It allows the researcher to assess how well the observed data fits the expected distribution across the three locations.

C (5) YOUR ANSWER

A degrees of freedom value of 5 would suggest there are six categories in the test, which is inconsistent with the three locations provided (A, B, and C). This overestimation does not align with the actual data and would lead to an incorrect conclusion in the hypothesis testing.

D (6) YOUR ANSWER

This choice implies there are seven categories (6 + 1), which is not the case here as there are only three locations being compared. Therefore, this value is incorrect and does not represent the appropriate calculation for degrees of freedom in this context.

Conclusion

In a goodness-of-fit test involving three categories, the degrees of freedom are determined by subtracting one from the number of categories. With three locations, the calculation leads to a degrees of freedom of 2, which is crucial for interpreting the results of the test correctly. Understanding this concept is vital for effectively analyzing data and drawing valid conclusions from statistical tests.

A researcher collected data on the preferences for the location of a major sporting event. The observed counts are: Location A: 310, B: 340, C: 350. Which value represents the degrees of freedom if a goodness-of-fit test is performed?

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

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