Consider the following hypothesis test:
H0: ≥ 10
Ha: < 10
The sample size is 140 and the population standard deviation is assumed known with σ= 6. Use α = .05.
a. If the population mean is 9, what is the probability that the sample mean leads to the conclusion do not reject H0 (to 4 decimals)?
b. What is the probability of making a type II error if the actual population mean is 8? (to 4 decimals)