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Question:
A manufacturer of salad dressings uses machines to dispense liquid ingredients into bottles that move along a filling line. The machine that dispenses dressings is working properly when the mean amount dispensed is 330 mL. The population standard deviation of the amount dispensed is 4 mL. A sample of 50 bottles is selected periodically, and the filling line is stopped if there is evidence that the mean amount dispensed is different from 330 mL. Suppose that the mean amount dispensed in a particular sample of 50 bottles is 329.7 mL.
a) Perform a hypothesis test (using either the p-value approach or critical value approach) to see if there is evidence that the population mean amount is different from 330 mL. (Use a 0.05 level of significance).
b) What would be your answer in (a) if the standard deviation is instead 0.9 mL?
c) What would be your answer in (a) if the sample mean is 328.9 mL and the standard deviation is 3 mL?
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