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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)

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