# Math Help - the probability of making a type II error CALCULATE BETA

1. ## the probability of making a type II error CALCULATE BETA

You draw one observation from a normal distribution with known variance 1. You want to test if mu = 0.
a) Find c such that if you reject H0 when |x| > c, you get alfa to be 0.05.
b) With this rejection region, calculate beta (the probability of making a type II error) if the true value of mu is 0.2,
Answer in the form 3.54,0.64 using 2 decimals.

2. First of all, since you are rejecting the null with alpha=.05 the rejection region is

$(-\infty,-1.96)\cup (1.96,\infty)$

since $.05=P(|X|>1.96)$

Now, $\beta=P(-1.96 when the MOO is .2 and variance is 1.

so you need to standardize appropriately...

$\beta=P(-1.96

$=P(-2.16

I don't know what this '3.54,0.64' is