Question: It is known that the variable X ~ N ( population mean, 1 6 ) . It is desired that the null hypothesis population mean

It is known that the variable X ~ N(population mean,16).
It is desired that the null hypothesis population mean=12 be tested against the alternative hypothesis population mean =12 with probability of a Type I error of 1%. A random sample of 15 observations of X is taken and the sample mean is taken to be the test statistic.
a. Find the acceptance and rejection regions in terms of sample mean .
b. For the case of population mean=15, find the probability of a type II error and the power of the test

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