# Suppose X ? N ( ? , 36 ) . From a sample of size n = 16, we wish to test H 0 : ? = 5 v s . H...

## Question:

Suppose {eq}X \sim N(\mu , 36) {/eq} . From a sample of size n = 16, we wish to test {eq}H_0: \mu = 5 vs. H_1: \mu > 5 {/eq}

a. What is the rejection region for a test of size .05?

b. What is the power of your test if mu = 6?

## Power of a test

Power of the test defines the probability that the null hypothesis would be rejected correctly. This infers that alternate hypothesis was true and hence the null is correctly rejected. It is calculated as the complement of the type II error rate, which defines the probability of accepting the null hypothesis given it is false.

## Answer and Explanation:

Given Information

{eq}X \sim N\left( {\mu ,36} \right) {/eq}

Sample size is 16 (n)

Hypotheses is given as,

{eq}\begin{align*} {H_o}:\mu =...

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