Consider the test of H0 2 5 againstH1 2

Consider the test of H₀: ² = 5 againstH₁: ² <5. Approximate the P-value for each of the following test statistics.

(a) Xo^2= 25.2 and n = 20

(b) Xo^2= 15.2 and n = 12

(c) Xo^2= 4.2 and n = 15

Solution

for p value we calculate

p= 1-P( X <= x ) where X follows Chi square distribution with n-1 degrees of freedom

where x is the observed value of the test statistic

Here

a) p value=0.154064

b)p value=0.230681

c)p value=0.99705