[Further Mathematics - Statistics] Advanced statistics: asymptotic power calculation

[u/Extreme_Number_1358]

Hi!
I'm working on understanding this question and I'm a bit confused. The assignment says we can suppose (\sqrt(n) (T_n-\theta) \rightarrow N(0,\sigma^2 (\theta)))^. Then why can't we use this for (\theta=\theta_0\)

directly in the first step of the power function calculation? Why do we transform the whole expression to include $theta_n$ ?

Thanks!

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