We begin by examining the data given:
The chi-square statistic (ChiSq) is provided directly:
[tex]\[ \chi^2 = 10.722 \][/tex]
Next, we must determine the degrees of freedom ([tex]\(df\)[/tex]) for this chi-square test. The degrees of freedom in a chi-square test for an [tex]\(r \times c\)[/tex] contingency table is calculated as:
[tex]\[ df = (r-1) \times (c-1) \][/tex]
where [tex]\( r \)[/tex] is the number of rows and [tex]\( c \)[/tex] is the number of columns.
In our table:
- The number of rows ([tex]\(r\)[/tex]) is 2 (labeled as 1 and 2).
- The number of columns ([tex]\(c\)[/tex]) is 4 (labeled as C1, C2, C3, and C4).
Therefore, the degrees of freedom are:
[tex]\[ df = (2 - 1) \times (4 - 1) = 1 \times 3 = 3 \][/tex]
Next, we need to find the p-value corresponding to the chi-square statistic of 10.722 with 3 degrees of freedom. After referring to chi-square distribution tables or using appropriate statistical tools, we find:
[tex]\[ \text{p-value} = 0.013328146018433728 \][/tex]
Now we determine which range the p-value falls into:
- [tex]\(0.05 < p \leq 0.10\)[/tex]
- [tex]\(0.01 < p \leq 0.02\)[/tex]
- [tex]\(0.02 < p \leq 0.025\)[/tex]
- [tex]\(0.025 < p \leq 0.05\)[/tex]
- [tex]\(0.005 < p \leq 0.01\)[/tex]
Given the p-value:
[tex]\[ 0.013328146018433728 \][/tex]
Clearly:
[tex]\[ 0.01 < 0.013328146018433728 \leq 0.02 \][/tex]
Hence, the p-value falls into the range:
[tex]\[ \text{0.01 to 0.02} \][/tex]
Therefore, the correct answer is:
[tex]\[ \boxed{B. \text{between } 0.01 \text{ and } 0.02.} \][/tex]
