Q. 5 - The Practice of Statistics for AP

Question

T11.5. We compute the value of the${\chi }^2$statistic to be $6.58$. Assuming that the conditions for inference are met, the P-value of our test is

(a) greater than $0.20$

(b) between $0.10$ and $0.20$.

(c) between $0.05$ and $0.10$.

(d) between$0.01$ and $0.05$

(e) less than $0.01$

Step-by-Step Solution

Answer

$\text{ (c) Between }0.05\text{ and }0.10$

Step 1: Given Information

Need to find the $p$-value of our test.

Step 2: Explanation

Given:

${\chi }^2=6.58$

The variable race contains $4$ categories: White, Black, Hispanic, and Other

The degrees of freedom is the number of categories decreased by $1$:

$$\begin{gathered} d f=c-1 \\ =4-1 \\ =3 \end{gathered}$$

The P-value is the probability of obtaining the value of the test statistic, or a value more extreme. The P-value is the number (or interval) in the column title of the chi-square distribution table in the appendix containing the ${\chi }^2$-value in the row $d f=3$ :

$0.05<P<0.10$