9. 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?
Answer: B
The degrees of freedom for the goodness-of-fit test is 2.
In a goodness-of-fit test, the degrees of freedom is calculated as the number of categories minus one. In this case, there are three locations (A, B, and C), which leads to 3 - 1 = 2 degrees of freedom.
A) 1
This option incorrectly suggests that the degrees of freedom is 1. This would only be the case if there were two categories (2 - 1 = 1). Since there are three locations in this scenario, this option does not apply.
B) 2
This option is correct as it reflects the appropriate calculation for degrees of freedom in a goodness-of-fit test. With three categories, the formula (number of categories - 1) yields 2, making this the right answer.
C) 5
Option C is incorrect as it suggests an excessive number of degrees of freedom. With three categories, the maximum degrees of freedom cannot exceed 2, hence this number does not fit the requirements of the test.
D) 6
This option also does not apply to the situation presented. Similar to Option C, a value of 6 implies a much larger number of categories than are present in the data, making it an incorrect choice.
Conclusion
The correct answer, 2, accurately represents the degrees of freedom calculated from the given data on location preferences. All other options fail because they either miscalculate the formula or assume an incorrect number of categories, failing to align with the fundamental principles of a goodness-of-fit test.