Question

for a chi-squared distribution, find χ2 α such that (a) p(x2 > χ2 α)=0.01 when v = 21; (b) p(x2 < χ2 α)=0.95 when v = 6; (c) p(χ2 α < x2 < 23.209) = 0.015 when v = 10.

Answer 1

To find the value of χ²α for a chi-squared distribution, we need to use the given probabilities and degrees of freedom. (a) When v = 21 and p(x² > χ²α) = 0.01, the critical value χ²α ≈ 38.925. (b) When v = 6 and p(x² < χ²α) = 0.95, the critical value χ²α ≈ 12.591. (c) When v = 10 and p(χ²α < x² < 23.209) = 0.015, the critical values are χ²α ≈ 2.706 and χ²β ≈ 20.483.

Step-by-step explanation:

To find the value of χ²α for a chi-squared distribution, we need to use the given probabilities and degrees of freedom.

(a) When v = 21 and p(x² > χ²α) = 0.01, we can calculate the critical value using a chi-squared table or calculator. In this case, χ²α ≈ 38.925.

(b) When v = 6 and p(x² < χ²α) = 0.95, we can calculate the critical value as χ²α ≈ 12.591.

(c) When v = 10 and p(χ²α < x² < 23.209) = 0.015, we can find the two critical values that bound this probability range. In this case, χ²α ≈ 2.706 and χ²β ≈ 20.483.

Answer 2

To find specific values of χ2 α for different probabilities and degrees of freedom in the chi-squared distribution The critical values are 4.54 and 17.709.

Step-by-step explanation:

For a chi-squared distribution:

a) To find χ2 α such that p(x2 > χ2 α) = 0.01 when v = 21, we need to find the critical value of χ2 α from the chi-squared distribution table. The critical value is 29.65.

b) To find χ2 α such that p(x2 < χ2 α) = 0.95 when v = 6, we need to find the critical value of χ2 α from the chi-squared distribution table. The critical value is 2.14.

c) To find χ2 α such that p(χ2 α < x2 < 23.209) = 0.015 when v = 10, we need to find the critical values of χ2 α from the chi-squared distribution table. The critical values are 4.54 and 17.709.