Question

You intend to conduct a goodness-of-fit test for a multinomial distribution with 6 categories. you collect data from 72 subjects. what are the degrees of freedom for the χ ²distribution for this test? d.f. =

Answer 1

The degrees of freedom for a chi-square goodness-of-fit test with 6 categories is 5. This is computed by taking the number of categories (6) and subtracting one.

Step-by-step explanation:

You are conducting a goodness-of-fit test for a multinomial distribution with 6 categories, and you have collected data from 72 subjects. For this type of test, which falls under the chi-square test, we calculate the degrees of freedom (df) by subtracting 1 from the number of categories. Therefore, the degrees of freedom for your test would be:

df = number of categories - 1

df = 6 - 1

df = 5

So, the degrees of freedom for the χ² distribution for this goodness-of-fit test would be 5. Remember that each category should have an expected value of at least five to effectively use this test, and the test is typically right-tailed.

Answer 2

In a goodness-of-fit test for a multinomial distribution with 6 categories, the degrees of freedom are 5, calculated as the number of categories minus 1.

Step-by-step explanation:

The student is conducting a goodness-of-fit test for a multinomial distribution with 6 categories using data from 72 subjects. The degrees of freedom (d.f.) for the chi-square (χ²) distribution in a goodness-of-fit test are determined by subtracting 1 from the number of categories.

In this case, the degrees of freedom for the χ² distribution would be 6 - 1 = 5. It is important to note that the expected value for each category should be at least five to validly use this test, which should not be an issue when the total number of subjects is 72.