Say that we have two datapoints x and y. Both x and y are independently normally distributed with variance 1. The mean of x is µ x and the mean of y is µ y. 1. You have a null hypothesis of µ x = µ y...

Say that we have two datapoints x and y. Both x and y are independently normally distributed with variance 1. The mean of x is µ_x
and the mean of y is µ_y.

1. You have a null hypothesis of µ_x= µ_y. You will reject if |x − y| > 2. What is the type I error rate of this test?

2. You have a null hypothesis of µ_x= µ_y. You will reject if
|x − y|
>
2.
If µ_x
- µ_y
= 10, what is the type II error rate of this test?

Extracted text: Say that we have two datapoints x and y. Both x and y are independently normally distributed with variance 1. The mean of x is µ, and the mean of is ly. 1. You have a null hypothesis of ug = ly. You will reject if |x – y| > 2. What is the type I error rate of this test? You have a null hypothesis of He = Hy. You will reject if |x – y| > 2. If 10, what is the type II error rate of this test? 2. Hx - Hy =