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I have a doubt in basic hypothesis testing. Suppose I have a testing setup as below. I have assumed null hypothesis that my sampling distribution has $\mu = 60$, and I get a sample set with sample mean at $\overline{x} = 62.75$

enter image description here

Now to evaluate my hypothesis, if discrete distribution, I would simply look up at $p(\overline{X} = 62.75)$ and if that is less than $\alpha$ we reject null or otherwise.

Since it is continuous, $p(\overline{X} = 62.75)$ is 0. But why instead of doing a continuity correction around 62.75, we take all probabilities above 62.75? What is the justification for that?

I am not able to justify why we leave the whole blue area. I understand my alternate hypothesis is $\mu > 60$, but not $\mu > 62.75$ or something like that. So its confusing.

Kindly clarify.

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  • $\begingroup$ How would you apply a countinuity correction on a continuous scale? Infinitesimally small intervals will give you infinitesimally small values. Large intervals just make no sense, there is no justification for them. $\endgroup$ Oct 4 '18 at 14:05
  • $\begingroup$ So we apply right tail area because continuity correction is not possible? $\endgroup$ Oct 4 '18 at 14:18
  • $\begingroup$ about continuity correction: people.stern.nyu.edu/jsimonof/classes/1305/pdf/contcorr.pdf $\endgroup$ Oct 4 '18 at 14:22

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