Question: (25 marks) It is given that X - N(µ,16). It is desired to test the null hypothesis µ = 12 against the alternative hypothesis µ > 12, with the probability of a Type I error being 1%. A random sample of 15 observations (sample size) of X is taken and the sample mean X ^¯ is taken to be the test statistic.

1. Find the acceptance and rejection regions.
2. For the case µ = 15, find the probability of a Type II error.
3. Derive and state the power function for µ > 12.
4. Compute the minimum sample sizes for power(15) > 0.9 and power(15) > 0.99.

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