When does a MP level-alpha test not exist?
I’m currently reading about the Neyman-Pearson Lemma for the MP level-$alpha$ test. My question is, when does there not exist a MP level-$alpha$ test?
For example, suppose that $X_1,...,X_n$ are iid $N(mu,sigma^2)$ where $sigma$ is known, $mu_0<mu_1$, and $mu_0=mu$ is the null hypothesis. The particular question I’m working on asks if there’s any $alpha$ for which a MP test exists, but after setting up the ratio of likelihood functions with alternative over null, I’m not sure why such a test wouldn’t exist. What must I check for and why?
statistics statistical-inference hypothesis-testing
asked Nov 26 at 11:52
DavidS
337111
add a comment |
I’m currently reading about the Neyman-Pearson Lemma for the MP level-$alpha$ test. My question is, when does there not exist a MP level-$alpha$ test?
For example, suppose that $X_1,...,X_n$ are iid $N(mu,sigma^2)$ where $sigma$ is known, $mu_0<mu_1$, and $mu_0=mu$ is the null hypothesis. The particular question I’m working on asks if there’s any $alpha$ for which a MP test exists, but after setting up the ratio of likelihood functions with alternative over null, I’m not sure why such a test wouldn’t exist. What must I check for and why?
statistics statistical-inference hypothesis-testing
asked Nov 26 at 11:52
DavidS
337111
What exactly are you testing? What is the alternative?
– StubbornAtom
Nov 26 at 13:11
The null hypothesis is provided. The alternative hypothesis is that $mu=mu_1$.
– DavidS
Nov 26 at 13:17
What did you get as the likelihood ratio? These should have been added in the post itself IMHO.
– StubbornAtom
Nov 26 at 13:21
Should’ve been in the post but I’m typing on an iPad (Computer was stolen), and so I tried providing the “minimally sufficient” info for the question. Will edit soon.
– DavidS
Nov 26 at 16:11
add a comment |
I’m currently reading about the Neyman-Pearson Lemma for the MP level-$alpha$ test. My question is, when does there not exist a MP level-$alpha$ test?
For example, suppose that $X_1,...,X_n$ are iid $N(mu,sigma^2)$ where $sigma$ is known, $mu_0<mu_1$, and $mu_0=mu$ is the null hypothesis. The particular question I’m working on asks if there’s any $alpha$ for which a MP test exists, but after setting up the ratio of likelihood functions with alternative over null, I’m not sure why such a test wouldn’t exist. What must I check for and why?
statistics statistical-inference hypothesis-testing
asked Nov 26 at 11:52
DavidS
337111
I’m currently reading about the Neyman-Pearson Lemma for the MP level-$alpha$ test. My question is, when does there not exist a MP level-$alpha$ test?
For example, suppose that $X_1,...,X_n$ are iid $N(mu,sigma^2)$ where $sigma$ is known, $mu_0<mu_1$, and $mu_0=mu$ is the null hypothesis. The particular question I’m working on asks if there’s any $alpha$ for which a MP test exists, but after setting up the ratio of likelihood functions with alternative over null, I’m not sure why such a test wouldn’t exist. What must I check for and why?
statistics statistical-inference hypothesis-testing
statistics statistical-inference hypothesis-testing
asked Nov 26 at 11:52
DavidS
337111
asked Nov 26 at 11:52
DavidS
337111
edited Nov 26 at 13:07
asked Nov 26 at 11:52
DavidS
337111
asked Nov 26 at 11:52
DavidS
337111
asked Nov 26 at 11:52
DavidS
337111
337111
What exactly are you testing? What is the alternative?
– StubbornAtom
Nov 26 at 13:11
The null hypothesis is provided. The alternative hypothesis is that $mu=mu_1$.
– DavidS
Nov 26 at 13:17
What did you get as the likelihood ratio? These should have been added in the post itself IMHO.
– StubbornAtom
Nov 26 at 13:21
Should’ve been in the post but I’m typing on an iPad (Computer was stolen), and so I tried providing the “minimally sufficient” info for the question. Will edit soon.
– DavidS
Nov 26 at 16:11
add a comment |
What exactly are you testing? What is the alternative?
– StubbornAtom
Nov 26 at 13:11
The null hypothesis is provided. The alternative hypothesis is that $mu=mu_1$.
– DavidS
Nov 26 at 13:17
What did you get as the likelihood ratio? These should have been added in the post itself IMHO.
– StubbornAtom
Nov 26 at 13:21
Should’ve been in the post but I’m typing on an iPad (Computer was stolen), and so I tried providing the “minimally sufficient” info for the question. Will edit soon.
– DavidS
Nov 26 at 16:11
What exactly are you testing? What is the alternative?
– StubbornAtom
Nov 26 at 13:11
What exactly are you testing? What is the alternative?
– StubbornAtom
Nov 26 at 13:11
The null hypothesis is provided. The alternative hypothesis is that $mu=mu_1$.
– DavidS
Nov 26 at 13:17
The null hypothesis is provided. The alternative hypothesis is that $mu=mu_1$.
– DavidS
Nov 26 at 13:17
What did you get as the likelihood ratio? These should have been added in the post itself IMHO.
– StubbornAtom
Nov 26 at 13:21
What did you get as the likelihood ratio? These should have been added in the post itself IMHO.
– StubbornAtom
Nov 26 at 13:21
Should’ve been in the post but I’m typing on an iPad (Computer was stolen), and so I tried providing the “minimally sufficient” info for the question. Will edit soon.
– DavidS
Nov 26 at 16:11
Should’ve been in the post but I’m typing on an iPad (Computer was stolen), and so I tried providing the “minimally sufficient” info for the question. Will edit soon.
– DavidS
Nov 26 at 16:11
add a comment |
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What exactly are you testing? What is the alternative?
– StubbornAtom
Nov 26 at 13:11
The null hypothesis is provided. The alternative hypothesis is that $mu=mu_1$.
– DavidS
Nov 26 at 13:17
What did you get as the likelihood ratio? These should have been added in the post itself IMHO.
– StubbornAtom
Nov 26 at 13:21
Should’ve been in the post but I’m typing on an iPad (Computer was stolen), and so I tried providing the “minimally sufficient” info for the question. Will edit soon.
– DavidS
Nov 26 at 16:11