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# Statistics 2 - Errors In Hypothesis Testing watch

1. I'm having some trouble getting my head around how the probabilities of Type I and II errors change as you alter the sample size or significance level of the test.

This is illustrated by the following question (OCR S2 June 2006 Q7, if that helps):

The first part asks you to calculate the critical region and Type II error probability of a normally distributed random variable, standard deviation 60.
The null hypothesis is that the mean is 4000, the alternative is that the mean is greater than 4000.
The sample size is 50 and the significance level 5%.

The actual mean is given as 4020, from which I calculated the probability of the error.

I've managed the first part, but it then asks two questions later about how the probability of a Type II error will change as:

1) The sample size is increased, but the significance level stays the same.

2) The significance level increases, but the sample size remains the same.

I can't seem to visualise how that would alter the rejection region and intersection of the two distributions.

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Updated: January 3, 2013
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