You conduct a hypothesis test for the mean of a population (h0 : p = 5) at the .05 significance level.
you establish a decision rule that you will reject this hypothesis if you get a sample mean greater than 7.
if, in reality, the population mean is 6, the probability of getting a sample mean greater than 7 is .73.

which of the following give you the probability of a type i error, the probability of a type ii error, and the power of the test, respectively?

a. 05; .73; .27

b. 27; .73; .05

c. 73; .05; .27

d. 27; .05; .73

e. 05; .27; .73

The correct option is a)

05; .73; .27 , type 1 error, type 11 error and the power of the test respectively.

Step-by-step explanation:

Alpha is the probability of a type 1 error, given the null hypothesis is true. Therefore alpha= 0.05

Type 11 error is the probability of accepting a false null hypothesis.

Beta= 0.73

The Power of a test is the probability of rejecting the null hypothesis, given it is false

Power= 1- beta

Power= 1-0.73

Power= 0.27

Therefore the type 1 error is 0.05

The type 11 error is= 0.73

The power of the test= 0.27

The right option is a)

the slope of the first function is -3. (3/1)

the slope of the second function is 1. (13-10/6-3).

since |-3| is greater than |1|, the function with the steepest slope is the first.