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I am unsure how to approach this problem:

Consider a random variable, X. Our hypothesis is that X~N(0,1) or X is standard normal distribution.

If we observe that X = 2.2. What is the likelihood of this hypothesis. Would the hypothesis be rejeted if we wanted to maintain a specificity of .95?

Thanks, RH

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    I don't understand your question. What do you mean by $X=2.2$? $X$ is a continuous random variable and hence the prob that takes on a particular value is zero...perhaps I am missing your point in the question...could you clarify it please?2012-09-22
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    I think the question is terribly worded. I believe that X = 2.2 means that an observation on X was recorded to be 2.2.2012-09-22
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    Ok. But even so, what do you plan to do with a single observation?2012-09-22
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    I think there are several imperfections in the way the question is phrased, but I completely disagree with the comments from Cristian and Rich H. That particular detail was clearly expressed. And I find Cristian's second comment somewhat obtuse.2012-09-22
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    You should try to explain better your problem! In hypothesis testing we usually have two hypothesis, the null and the alternative. Then you can compute things such as the likelihood ratio. But you did not give any alternative hypothesis, so we cannot do that. This leaves us with very little to work on, so pleas explain better.2012-09-22
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    @MichaelHardy I disagree. The question is not clear at all. First, the null is X normal; what is the alternative? X is chi-square? My guess was that Rich had in mind something along the lines of Dilip's answer. That's why I wrote my 1st comment. Rich then said that he believes X=2.2 is an observation on X, which made me think that he is dealing with samples, in which case you need a sample larger than one to get estimates of the mean and the variance of X. This is why I wrote my 2nd comment. Sorry if you think this is obtuse.2012-09-22

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