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GARP QA textbook question

smriti2232

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Hi, Can you please explain the solution to the following textbook question from hypothesis testing:

A data management group wants to test the null hypoth esis that observed data is N(0,1) distributed by evaluating the mean of a set of random draws. However, the actual underlying data is distributed as N(1, 2.25).
a. If the sample size is 10, what is the probability of a Type II error and the power of the test? Assume a 90% confidence level on a two-sided test.
b. How many samples would need to be taken to reduce the probability of a Type II error to less than 1%?
 
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