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 8 ounces. The population standard deviation of the amount dispensed is 0.15 ounce. 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 8 ounces. Suppose that the mean amount dispensed in a particular sample of 50 bottles is 7.983 ounces.
a. Is there evidence that the population mean amount is different from 8 ounces? (Use a 0.05 level of significance.)
b. Compute the p-value and interpret its meaning.
c. What is your answer in (a) if the standard deviation is 0.05 ounce?
d. What is your answer in (a) if the sample mean is 7.952 ounces and the standard deviation is 0.15 ounce?