The life insurance industry maintains that the average worker in Saskatoon has n

Question

The life insurance industry maintains that the average worker in Saskatoon has no more than $25,000 of personal life insurance. You believe it is higher. You sample 100 workers in Saskatoon at random and find the sample average to be $26, 650 of personal life insurance. The population standard deviation is known to be $12,000. Use alpha = 0.05 throughout. Test your belief using a significance level of 5%. Explain, in the context of this question, what is meant by a Type I error, a Type II error, and the power of the test? If the true average for this population is in fact $30,000, what is the probability of committing a Type II error? Calculate the power of the test.

Explanation / Answer

ans=

H0=25000

H1>25000

Z=(26650-25000)/(12000/sqrt 100)

=1.375

Z0.05=1.64

since 1.375 is less than 1.64 accept H0

6)type I error is committed when the statement that the average worker in Saskatoon has no more than $25,000 of personal life insurance is rejected when it is true.

type II error is committed when the statement that the average worker in Saskatoon has no more than $25,000 of personal life insurance is accepted when it is false.

power of the test is the probability of not committing type II error

5)beta=(26650-30000)/(12000/sqrt100)=-2.79

P(Z<-2.79)=0.0026

2)power of the test=1-0.0026

    =0.9974

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