S
StevieG4captain
Member
Think I'm being dumb, but would really appreciate it if anyone could clear up the following for me:
Chapter 12 - Hypothesis Testing
2 Classical testing, significance and p-values
2.1 'Best' tests
Regarding the Neyman-Pearson Lemma, Im not sure how the following criteria gives the test statistics for the mean mu and the variance sigma^2:
[max(Likelihood under H0)]/[max(Likelihood under H0+H1)] < critical value
In the case of the mean mu:
I make the max(Likelihood under H0): mu0hat=Xbar
and the max(Likelihood under H0+H1): muhat=Xbar
How this method leads to the test statistics:
[Xbar-mu0]/[S/n^0.5]~t{n-1} under H0: mu=mu0
or [(n-1)S^2]/[sigma0^2]~chisqr{n-1} under H0: sigma^2=sigma0^2
I do not know
Maybe I just need some sleep, but if anybody knows it would save me a great deal of time!
Thanks (in anticipation)
Chapter 12 - Hypothesis Testing
2 Classical testing, significance and p-values
2.1 'Best' tests
Regarding the Neyman-Pearson Lemma, Im not sure how the following criteria gives the test statistics for the mean mu and the variance sigma^2:
[max(Likelihood under H0)]/[max(Likelihood under H0+H1)] < critical value
In the case of the mean mu:
I make the max(Likelihood under H0): mu0hat=Xbar
and the max(Likelihood under H0+H1): muhat=Xbar
How this method leads to the test statistics:
[Xbar-mu0]/[S/n^0.5]~t{n-1} under H0: mu=mu0
or [(n-1)S^2]/[sigma0^2]~chisqr{n-1} under H0: sigma^2=sigma0^2
I do not know
Maybe I just need some sleep, but if anybody knows it would save me a great deal of time!
Thanks (in anticipation)