Q. 1 - The Practice of Statistics for AP

Question

A chi-square goodness-of-fit test is used to test whether a 0 to 9 spinner is "fair" (that is, the outcomes are all equally likely). The spinner is spun 100 times, and the results are recorded. The degrees of freedom for the test will be

(a) 8 .

(c) 10 .

(e) None of these.

(b) 9 .

(d) $99 .$

Step-by-Step Solution

Answer

(b) The degrees of freedom for the test is $9$.

Step 1: Given Information

Need to find the degrees of freedom for the test.

Step 2: Explanation

We have been given a 0 to 9 spinner, which has 10 possible outcomes: $0,1,2,3,4,5,6,7,8,9.$

This then implies that there are 10 possible categories for the variables.

$c=10$

The degrees of freedom for the (chi-square goodness-of-fit) test is then the number of categories decreased by $1 .$

$$\begin{gathered} d f=c-1 \\ =10-1 \\ =9 \end{gathered}$$