Question

True or False:

(a) The generalized likelihood ratio statistic Λ (the one we use when the hypotheses are composite, i.e., we must use the MLE estimator in the denominator) is always less than or equal to 1.

(b) If the p-value is 0.03, the corresponding test will reject at the significance level 0.02.

(c) If a test rejects at significance level 0.06, then the p-value is less than or equal to 0.06.

(d) The p-value of a test is the probability that the null hypothesis is correct.

(e) In testing a simple versus simple hypothesis via the likelihood ratio, the p-value equals the likelihood ratio.

(f) If a chi-square test statistic with 4 degrees of freedom has a value of 8.5, the p-value is less than 0.05.

Answer 1

a) True

b) False

If p value < significance level (alpha) then we reject test

If p value > significance level then we fail to reject the test

Here p value = 0.03 > alpha = 0.02 , we fail to reject null hypothesis

c) True

d) False

P value is conditional probability given null hypothesis is true.

e) False

The p-value is a probability computed assuming the null hypothesis is true.For the likelihood ratio test,it is the probability that the likelihood ratio(H0toH1)is smaller than the observed value,computed under the conditional probability given H0.

f) False

In excel using command "CHIDIST(8.5,4)" , we will get p value =0.07488

P value is greater than 0.05.