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Old 9th June 2012, 12:17 PM   #1 (permalink)
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Some questions about hypothesis testing

Just some questions on hypothesis testing:

1. What is the rationale of rejecting H0 when p-value < level of significance? I know that the p-value is the probability of obtaining a test statistic at least as extreme as the observed value while assuming H0 is true, and that the level of significance is the probability of rejecting H0 when it is in fact true. My way of thinking is that if the p-value is low then it provides little credence for H0 being true and if it is less than the level of significance, then it is sort of "safe" to reject H0. Is this correct?

2. What exactly is a 4-test / t-distribution and its associated degrees of freedom? My notes don't offer an explanation and searching the web just made me more confused.

3. Why must a t-test be used when the population variance is unknown and the sample size is small? Why is a z-test no longer appropriate under such conditions?

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Old 12th June 2012, 12:27 PM   #2 (permalink)
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Re: Some questions about hypothesis testing

2. im gonna agree based off remote memory. assuming level of significance of 0.05, if p-value is less than that, at say 0.04, yes, that is in the rejection region.

2. it is just another method of estimation depending on what information you have at hand. its degrees of freedom is essentially an estimation of the standard deviation if you don't have that value.

3. this is how i think about it. if your sample size is small, how dependable is your variance? so essentially, when you have small size, you don't know your variance. and when you don't know your variance, you can't use normal distribution. hence, use t-distribution.

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