4. The supervisor of the Food Court at the Union suspectsthat one of the hamburg

Question

4. The supervisor of the Food Court at the Union suspectsthat one of the hamburger suppliers is delivering patties thatweigh less than the required 16 ounces each. He is going todetermine that the patties weigh less than 16 ounces if his sampleof 50 patties has a mean weight under 15.85 ounces. Assumethe standard deviation of the population is .4 ounces.

a. What is the power against an alternative mean of15.72 ounces? In other words, if the mean is really 15.72ounces, what is the chance you will detect this and reject the nullhypothesis?

b. What is the alpha error of the hypothesistest?

c. What is the probability that the null hypothesisof m = 16 is true but you reject it?

d. What is the probability that the null hypothesisof m = 16 is false but you accept it?

e. What is the probability that the null hypothesisof m = 16 is true and you accept it?

f.       If you had sampled only 25patties rather than 50, what would happen to the power of yourhypothesis test?

Explanation / Answer

a) find area under normal curve with mean 15.72 and std.4/(50) from 15.85 to infinity normalcdf(15.85,1E99,15.72,.4/(50)) = .0108 = Power = 1- = 0.9892 b) find area under normal curve with mean 16 and std .4/(50from -infinity to 15.85 normalcdf(-1E99,15.85,16,.4/(50)) = .0040 = c) = 0.0040 d) = 0.0108 e) 1-- = 0.9852 f) find area under normal curve with mean 15.72 and std.4/(25) from 15.85 to infinity normalcdf(15.85,1E99,15.72,.4/(25)) = .0521 = Power = 1- = 0.9479

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