Question: Suppose we randomly sample n = 50 numbers X1, . . . , X100 from a N(, ) distribution where is known to be 3.

Suppose we randomly sample n = 50 numbers X1, . . . , X100 from a N(, ) distribution where is known to be 3. We wish to test the hypotheses H null: = 2 and H alternative: != 2 at a significance level of = 0.05. If the real value of is 4 then what is the theoretical power of this test? calculate with R code.

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