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.
We now want to test
\displaystyle \displaystyle H_0\, :\, \lambda =0.03 \displaystyle \text {vs} \displaystyle H_1\, :\, \lambda \neq 0.03
at (significance) level \alpha =5\%.
Write down the chi-square distributed test statistic T_{n,\text {Wald}} for Wald's test, in terms of \hat{\lambda }^{\text {MLE}}, n. To avoid double jeopardy, you may also enter the answer in terms of the Fisher information I=I(\hat{\lambda }^{\text {MLE}}).
(Enter hatlambda for \hat{\lambda }^{\text {MLE}} and I for I=I(\hat{\lambda }^{\text {MLE}}).)
T_{n}^{\text {Wald}}=\quad
unanswered
Find the p-value p^{\text {Wald}} for Wald's test.
(Enter a numerical answer accurate to at least 2 decimal places.)
p^{\text {Wald}}=\quad