Hypothesis testing - maximum significance level

Georgegr

New member
Joined
Nov 4, 2018
Messages
6
Hi to everyone! I need a clarification of the sentence included in bold. Is that the error type II? The exercise is:


The weight of a plate is a continuous random variable, normally distributed with [FONT=MathJax_Math]μ[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]330[/FONT]gr. and standard deviation 5 gr.
Supposing that we have a sample of 25 plates with a mean weight of 333 gr., sample variance of 25 gr. and a significance level of 10%, check the hypothesis that [FONT=MathJax_Math]μ[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]330[/FONT]or [FONT=MathJax_Math]μ[/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]330[/FONT].

What is the maximum significance level that the null hypothesis is not rejected?
 
Hi to everyone! I need a clarification of the sentence included in bold. Is that the error type II? The exercise is:

The weight of a plate is a continuous random variable, normally distributed with [FONT=MathJax_Math]μ[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]330[/FONT]gr. and standard deviation 5 gr.
Supposing that we have a sample of 25 plates with a mean weight of 333 gr., sample variance of 25 gr. and a significance level of 10%, check the hypothesis that [FONT=MathJax_Math]μ[/FONT][FONT=MathJax_Main]=[/FONT][FONT=MathJax_Main]330[/FONT]or [FONT=MathJax_Math]μ[/FONT][FONT=MathJax_Main]>[/FONT][FONT=MathJax_Main]330[/FONT].

What is the maximum significance level that the null hypothesis is not rejected?

The significance level is the probability of a type I error (rejecting a true null hypothesis).

I think the question would be better phrased as "What is the maximum significance level at which the null hypothesis is not rejected?"

Suppose they gave you a significance level, say 5%. How would you decide whether to reject the null hypothesis?

For what significance levels will you not reject the null hypothesis? Note that if you set a really high significance level (say, 100%), you would always reject the null hypothesis; so there must be a maximum at which you would not (for the given data).

That is what it is asking for.
 
Top