Question

Consider the following hypotheses tests involving the χ²-distribution.

(a) Determine the p-value for H_o: P(1) = P(2) = P(3) = P(4) = 0.25, with χ² = 5.85. (Give your answer bounds exactly.)
< p <

(b) Determine the p-value for H_o: P(I) = 0.25, P(II) = 0.40, P(III) = 0.35, with χ² = 5.34. (Give your answer bounds exactly.)
< p <

Answer 1

a) Under H₀, the test statistic follows a chi square distribution with 4 -1 = 3 df.

p-value

So, 0.10 < p-value < 0.15

b) Under H₀, the test statistic follows a chi square distribution with 3 -1 = 2 df.

p-value

So, 0.05 < p-value < 0.10