Determining sample size needed to test hypothesis

In summary, the 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. He needs to 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.
  • #1
Orikon
12
0
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
 
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  • #2
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...
 
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  • #3
ksinclair13 said:
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
 
  • #4
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?
 
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  • #5
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?
 
  • #6
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...
 
  • #7
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...
 

1. How do you determine the appropriate sample size for a hypothesis test?

The appropriate sample size for a hypothesis test depends on several factors, including the desired level of confidence, the expected effect size, and the variability of the population. Generally, a larger sample size is needed for a higher level of confidence and a smaller expected effect size. Statistical power analysis can be used to determine the sample size needed for a specific hypothesis test.

2. What is the significance of sample size in hypothesis testing?

Sample size is a crucial factor in hypothesis testing as it affects the accuracy and reliability of the results. A small sample size may not accurately represent the population, leading to incorrect conclusions. On the other hand, a larger sample size can increase the statistical power and reduce the margin of error in the results.

3. Can a small sample size affect the validity of a hypothesis test?

Yes, a small sample size can affect the validity of a hypothesis test. If the sample size is too small, the results may not be representative of the population, leading to biased or inaccurate conclusions. It is important to ensure that the sample size is large enough to provide reliable results.

4. How does the type of hypothesis being tested affect the sample size needed?

The type of hypothesis being tested can affect the sample size needed in several ways. For example, a one-tailed hypothesis test may require a smaller sample size compared to a two-tailed test, as the latter considers both positive and negative effects. Additionally, the complexity of the hypothesis and the number of variables being tested can also impact the required sample size.

5. Is there a specific formula for calculating the sample size needed for a hypothesis test?

Yes, there are several formulas that can be used to calculate the sample size needed for a hypothesis test, such as the one for a one-sample t-test or the one for a two-sample t-test. These formulas take into account the desired level of confidence, expected effect size, and standard deviation of the population. It is recommended to consult a statistician or use a statistical power calculator to determine the appropriate sample size for a specific hypothesis test.

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