Question

can a critical value for the chi-square test be negative? explain.

choose the correct answer below.

a. no, in a chi-square distribution, all \\(\chi^2\\)-values are greater than or equal to 100.

b. no, in a chi-square distribution, all \\(\chi^2\\)-values are greater than or equal to 0.

c. yes, in a chi-square distribution, half of the \\(\chi^2\\)-values are less than 0, and half of the \\(\chi^2\\)-values are greater than 0.

d. yes, in a chi-square distribution, all \\(\chi^2\\)-values are less than 0.

Explanation:

To determine if a chi - square critical value can be negative, we recall the properties of the chi - square distribution. The chi - square statistic \(\chi^{2}\) is calculated as the sum of squared standard normal variables. Since squaring a real number always results in a non - negative number (i.e., \(x^{2}\geq0\) for any real \(x\)), and the chi - square value is a sum of such squared terms, all \(\chi^{2}\) values (including critical values) are greater than or equal to 0.

• Option A is incorrect because there is no requirement for \(\chi^{2}\) values to be greater than or equal to 100.
• Option C is incorrect as chi - square values are non - negative, so they can't be less than 0.
• Option D is incorrect because chi - square values are non - negative, not less than 0.

Only Option B correctly states the property of the chi - square distribution.

Answer:

B. No, in a chi - square distribution, all \(\chi^{2}\) - values are greater than or equal to 0.