Calculate the likelihood ratio for Example B of Section 9.6 and compare the results of a test based on the likelihood ratio to those of one based on Pearson's chi-square statistic.
Suppose that a test statistic T has a standard normal null distribution.
a If the test rejects for large values of [T] what is the p-value corresponding to T = 1.50?
b Answer the same question if the test rejects for large T.
True or false:
a The generalized likelihood ratio statistic A is always less than or equal to 1.
b If the p-value is .03, the corresponding test will reject at the significance level .02.
c If a test rejects at significance level .06, then the p-value is less than or equal to .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 .05.