Question

Consider a random sample from a normal population with mean u = 3 and variance o2 = 22, with sample size n = 20. Suppose the sample variance is 82 = 2.72. Let p be the probability that s2 exceeds the sample variance 52. Which of the following is true? 0.01 < p < 0.025 0.025 < p < 0.05 0.05<P 0.005< p < 0.01 Op < 0.005

Answer 1

We know that

(n-1) 02 2 Xn-1

Now,

$\\\rho=P(S^2>s^2)=P(S^2>2.7^2)=P(\frac{(n-1)S^2}{\sigma^2}>\frac{(20-1)2.7^2}{2^2})\\ \\ =P(\chi_{19}^2>34.628)=0.015$

Hence $0.01<\rho<0.025$ .

Hence 1st option.