The lifetime (in thousands of hours) X of a light bulb has pdf
g(x)= \lambda e^{-\lambda x}, \hspace{3mm} x\geq 0
for some unknown \lambda >0.
We collect {\color{blue}{n=33}} independent lightbulbs at random and record their lifetime X_1,\ldots ,X_ n, which are all independent copies of X. We find that {\color{blue}{\overline{X_ n}=42.6}} thousand hours.
Write down the test statistic T_{n,\text {LR}} for the likelihood ratio test, in terms of \hat{\lambda }^{\text {MLE}}, n.
(Enter hatlambda for \hat{\lambda }^{\text {MLE}} and S_n for S_ n=\sum _{i=1}^ n X_ i.)
T_{n}^{\text {LR}}=\quad
unanswered
What is p-value p^{\text {LR}} of the likelihood ratio test?
(Enter an answer accurate to at least 3 decimal places.)
p^{\text {LR}}=\quad
What is the conclusion of the Likelihood Ratio test?
(Read the choices carefully, especially the subscripts.)
Reject H_0
Do not reject H_0.
Conclude H_0 is true.
Reject H_1
Do not reject H_1.
Conclude H_1 is true.