Question

Mean amount of milk in a bottle that was filled by a set of 32 aun with a standard deviation of 0.06 aun. Suppose the mean amount of milk widely distributed normally. To ensure that the machine operates well, 36 bottles containing milk randomly and mean amount of milk obtained.

a) if test with α = 0.05 is carried out to determine whether the machine works well, specify the criteria of the test rejection.

b) About the power of the test if the mean population are:

i) 31.97

ii) 31.99

iii) 32.00

iv)32.01

v) 32.03 Draw of power test above.

c) Calculate the probability of type II Error if the mean of a population is 32.03.

Answer 1

Using Minitab

stat -> power and sample size -> 1-sample z

Power and Sample Size

1-Sample Z Test

Testing mean = null (versus ≠ null)
Calculating power for mean = null + difference
α = 0.05 Assumed standard deviation = 0.06

            Sample
Difference    Size     Power
     -0.03      36 0.850839
     -0.01      36 0.170075
      0.00      36 0.050000
      0.01      36 0.170075
      0.03      36 0.850839

B)

type ii error = 1 - power

here diff = 0.03

hence

type ii error = 1 - 0.850839 = 0.1492