Can someone help me with part B of this question please? I am completely stuck and do not know how to proceed. Hints rather than answers appreciated please as this is allowed under my schools rules
I have defined what the score test is and made the substitutions according to the given value for $$E[-l"(B_0)] = \frac{n}{B_0}^2 $$ and the calculated value for $$(l'(B_0))^2 = ((\frac{n}{B_0} -\sum_{i=0}^n log(Xi))^2 $$. When plugging both into the value for the Score Statistic I get the following $$ S = ((\frac {n}{B_0} - \sum_{i=0}^n log(Xi))^2 * \frac{B_0^2}{n} $$ I am unsure how to remove the $B_0$ value in place for the MLE, $\hat{B}$. I evaluated the Score statistic under the Null Hypotehsis such that, $H_0: B = 1$ yet remain stuck how to proceed. I have tried the substitution $\sum_{i=0}^n log(Xi) = \frac{n}{\hat{B}} $ but this has got me nowhere
Written work of my current progress:
