Power of test: Polychlorinated biphenyls (PCBs) have been found to be dangerousl

Question

Power of test:

Polychlorinated biphenyls (PCBs) have been found to be dangerously high in some game birds found along the marshlands of the southeastern coast of the United States. The Federal Drug Administration(FDA) considers a concentration of PCBs higher than 5 parts per million(ppm) in these game birds to be dangerous for human consumption. A sample of 38 game birds produced an average of 7.2 ppm with a standard deviation of 6.2 ppm. Is there sufficient evidence to indicate that the mean ppm of PCBs in the population of game birds exceeds the FDA's recommendation limit of 5 ppm? Use a significance of 0:05

Explanation / Answer

a)

z>=(7.2-6/6.2/38)=1.19=1-0.8830=0.117. 0.117 is the probability of type 2 error and 0.8830 is the power of the test 1-B.

b)

z>=(7.2-7/6.2/38)=0.2=1-0.5793=0.4207. 0.4207 is the probability of type 2 error and 0.5793 is the power of the test 1-B.

c)

z>=(7.2-8/6.2/38)=-0.8=1-0.2119=0.7881. 0.7881 is the probability of type 2 error and 0.2119 is the power of the test 1-B.

z>=(7.2-9/6.2/38)=-1.79=1-0.0367=0.9633. 0.9633 is the probability of type 2 error and 0.0367 is the power of the test 1-B.

z>=(7.2-10/6.2/38)=-2.78=1-0.0027=0.9973. 0.9973 is the probability of type 2 error and 0.0027 is the power of the test 1-B.

z>=(7.2-12/6.2/38)=-4.77=1-0.0000=1. 1 is the probability of type 2 error and 0.0000 is the power of the test 1-B.

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