A production line operates with a mean filling weight of 500 grams per container. Over filling or under filling presents a serious problem and when detected requires the operator to shut down the production line to readjust the filling mechanism. From past data, a population standard deviation = 25 grams is assumed. A quality control inspector selects a sample of 30 items every hour and at that time makes the decision of whether to shut down the line for readjustment. The level of significance is a= 0.05.
a. State the hypotheses in the hypothesis test for this quality control application.
b. If a sample mean of 510 grams were found, what is the p-value? What action would you recommend?
c. If a sample mean of 495 grams were found, what is the p-value? What action would you recommend?
d. Use the critical value approach. What is the rejection rule for the preceding hypothsis testing procedure? Repeat parts (b) and (c). Do you reach the same conclusion?
(a) H0: The population mean is 500 grams vs Ha: The population mean is different from 500 grams, that is
H0: mu = 500 vs Ha: mu <> 500
(b) z = (x-bar - mu)/(s/sqrt n) = (510 - 500)/(25/sqrt 30) = 2.1909
Two-tailed p- value = 0.0285
Since 0.0285 < 0.05, we reject H0 ...
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