Determining sample size needed to test hypothesis

[Orikon]

This is a statistics and probability question.
I've been trying to figure this out for hours but I'm getting nowhere:
I have to test the hypothesis that the true average value of a sample is 6.2. I will reject the null hypothesis if with 95% confidence if the true average value is indeed 6.2 or reject the null hypothesis if the true average is 6.0.

I need to calculate the number of samples needed to test the hypothesis with the required accuracy, as well as the cut-off level, assuming a standard deviation of 0.4.

I have never done a problem where average value or sample size wasn't given, any help on how to get started would be greatly appreciated

 

[ksinclair13]

Can you type in the exact problem? I think I can help you on this, but I need to know the problem word for word first :).

Usually, you are given the margin of error for these kinds of problems...

 

[Orikon]

Can you type in the exact problem? I think I can help you on this, but I need to know the problem word for word first :).

sure,
An engineer wants to test the hypothesis that the true average voltage threshold V of a diode is 6.2 Volts as labeled.

He will accept the null hypothesis with 95% confidence if the true average voltage is indeed 6.2 Volts, and will reject the null hypothesis with 95% confidence if the true average voltage is instead 6.0 Volts

calculate the number of diodes that he will need to measure and the cut-off level for the voltage in order to test the hypothesis with the required accuracy. Assume the standard deviation of the diodes is 0.4V

Thanks in advance, appreciate your help

 

[ksinclair13]

Thank you :-)

Okay, if you were to write out a 95% confidence interval for this, how would you write it?

6.2 +- ??

Think about it. If you reject H₀ at 6.0, what value do you think goes in where the question marks are?

 

[Orikon]

ah ok, that would be 0.2, which is the margin of error right? then i can solve the equation for the sampe size...I got a value of 11 using a one tailed test. does that sound right to you, or do you think this is a two tailed.

Many thanks :)

by the way, I am still not sure how i would find the cutoff value, any ideas on that?

 

[ksinclair13]

It sounds one-sided, although it doesn't really say. Regardless, I don't think your answer is correct. I think you derived the correct equation, but I think you used the z* value of 1.645 (90% confidence) instead of 1.960 (95% confidence). Perhaps my memory has failed me...

 

[Orikon]

Actually, according to my handy table here, 1.645 is for a 95% one-sided confidence; 1.96 is used for two sided 95% confidence (corresponds to 97.5%). Anyways, thanks a lot, I can't believe I spent so much time on that lol. As for the cutoff level , what do you think they mean by that? I would guess 6.0 but that seems too easy...