Question

Mercury in Tuna ~ Mercury, if ingested can cause severe health problems. The amount of mercury in Tuna’s body tissue is much higher than other fish. It is known that the amount of mercury in Albacore tuna is normally distributed with mean 10.13 micrograms and standard deviation of 2.03 micrograms per ounce. A food company has a production line for canned albacore tuna. They regularly take random samples of 10 cans of tuna and test the amount of mercury. If the sample mean amount of mercury in tuna exceeds 11.6 micrograms per ounce, the production line will be stopped to find the source of contamination. Let μ denote the actual population mean amount of mercury in tuna per ounce. The hypotheses for this testing situation are: H0: μ = 10.13 vs HA: μ > 10.13. Note: Numbers are randomized for each instance of this question. Use the numbers given above. What is the power of the hypothesis test, using the decision rule given above, if the population mean amount of mercury is 11.0764 micrograms per ounce? Give your answer to 4 decimal places.

Answer 1

for normal distribution z score =(X-μ)/σ
here mean=       μ=	11.0764
std deviation   =σ=	2.030
sample size       =n=	10
std error=σx̅=σ/√n=	0.64194

power of the test =P(X>11.6)=P(Z>(11.6-11.0764)/0.642)=P(Z>0.82)=1-P(Z<0.82)=1-0.7926=0.2074