1. the probability of type 2 error will be affected by the choice of test statistics....

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Statistics

1. the probability of type 2 error will be affected by thechoice of test statistics. but why???
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A significance level corresponds to a certain value of thetest statistic say t represented by the orange line in thepicture of a sampling distribution below the picture illustrates ahypothesis test with alternate hypothesis 0Since the shaded area indicated by the arrow is the pvaluecorresponding to t that pvalue shaded area is To have pvalue less than a tvalue for this test must be tothe right of tSo the probability of rejecting the null hypothesis when it is trueis the probability that t t which we saw above is In other words the probability of Type I error is Rephrasing using the definition of Type I errorThe significance level is the probability of making the wrongdecision when the null hypothesis is truePros and Cons of Setting a Significance LevelSetting a significance level before doing inference has theadvantage that the analyst is not tempted to chose a cutoff on thebasis of what he or she hopes is trueIt has the disadvantage that it neglects that some pvaluesmight best be considered borderline This See Answer

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