A machine at AMT & Co. fills 120-ounce jugs with laundry softener. A quality con

Question

A machine at AMT & Co. fills 120-ounce jugs with laundry softener. A quality control inspector wishes to test if the machine needs an adjustment or not, which is needed when the machine either overfills or underfills the jugs. Assume the distribution of the amount of laundry softener in these jugs is Normal. Under “standard” circumstances, the mean amount should be 120 ounces with a standard deviation of 1 ounce. Suppose the quality control inspector wishes to conduct the test using = 0.10 and a sample size of 40. If the true mean amount of detergent in these jugs is 119.5 ounces, what is the power of the test?

Explanation / Answer

Here We will reject the null hypothesis which is = 120 ounces when we find sample mean x < 120 - Z0.90,two-tail * (/n) = 120 - 1.645 * (1/40) = 120 - 0.26 = 119.74 ounc

Here as standard erro of sample mean = (/n) = (1/40) = 0.26 ounces

so if true mean amount of detergent = 119.5 ounes

Power = Pr(x < 119.74) = Pr(x < 119.74 ; 119.5 ; 0.26)

Z = (119 .74 - 119.5)/ 0.26 = 0.9231

Power = Pr(x < 119.74) = Pr(x < 119.74 ; 119.5 ; 0.26) = Pr(Z < 0.9231) = 1 - 0.822 = 0.1780

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