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The Complete Idiot's Guide to Statistics, 2nd Edition by Robert Donnelly

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The Role of Alpha in Hypothesis Testing

For all the examples in these last two chapters, I have just stated a value for α, the level of significance. I’m sure you’re wondering what impact changing the value of α will have on the hypothesis test. Great question!
 
Suppose that I am making a claim that the average grade for a person using this book will be more than an 87. (I’m not really making this claim, so don’t get too excited!) I would state the hypothesis test as follows:
H 0 : µ ≤ 87
H1 : µ > 87
Now, it would be in my best interest if I could reject H0, which would validate my claim. I can do so by choosing a fairly high value for α, say 0.10. This corresponds to a critical z-score of +1.28, because we are using the right ...

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