- #1
GabrielN00
Homework Statement
Given [tex]X_1,\dots,X_n[/tex] a simple random sample with normal variables ([tex]\mu, \sigma^2[/tex]). We assume [tex]\mu[/tex] is known but [tex]\sigma^2[/tex] is unknown.
The hypothesis is
[tex]
\begin{cases}
H_0: & \mu=\mu_0 \\
H_1: & \mu=\mu_1 > \mu_0
\end{cases}
[/tex]
Determine the rejection region [tex] R[/tex] in order to minimize the [tex] P_{H_0}(R)+P_{H_1}(R^c)[/tex] .
Homework Equations
The Attempt at a Solution
I'm having problems both to understand the rejection regions and to find the minimum of the sum.The "plan" would be to consider [tex]z=\displaystyle\frac{\bar{X}-\mu}{(s/\sqrt{n})}[/tex]
I could proceed to do a one-tail test and find the minimum, but the very first problem is that my [tex]\alpha[/tex] value is unknown, so I cannot look it up in a table.
I'm clueless at even how to get a usable expression for each type error, since everything I am able to find suggest the use of a table, but the problem clearly doesn't make use of one.