Question

Consider the following hypothesis test.

H₀: U ≥ 10
H_a: U < 10

The sample size is 120 and the population standard deviation is assumed known with = 6. Use = .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 type of error would be made if the actual population mean is 9 and we conclude that H₀: ≥ 10 is true?
SelectType I errorType II errorItem 2

c. What is the probability of making a Type II error if the actual population mean is 8 (to 4 decimals)?

Answer 1

Ans:

sample mean cut off =10-1.645*(6/sqrt(120))=9.099

a)

z=(9.099-9)/(6/sqrt(120))

z=0.181

Reject H0,if z<0.181

Fail to reject H0,if z>0.181

P(z>0.181)=0.4283

b)

Type II error

(when we fail to reject Ho,but in fact Ho is false,we make type II error)

c)

z=(9.099-8)/(6/sqrt(120))

z=2.006

P(z>2.006)=0.0224