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One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. A
One company's bottles of grapefruit juice are filled by a machine that is set to dispense an average of 180 milliliters (ml) of liquid. A quality-control inspector must check that the machine is working properly. The inspector takes a random sample of 40 bottles and measures the volume of liquid in each bottle. The mean amount of liquid in the bottles is 179.6 ml and the standard deviation is 1.3 ml. We want to test 0: :=180180 where = the true mean volume of liquid dispensed by the machine. A significance test yields a -value of 0.0589. We choose to make a decision using =0.10 Because the -value of 0.0589 is less than =0.10, we reject 0 We have convincing evidence that the true mean volume of liquid dispensed by the machine is different from 180 ml. Would this conclusion change if a 5% significance level was used instead of a 10% significance level? No, it would not change because the -value is still less than . We would still reject 0. Yes, it would change because the -value is now greater than . Now we would fail to reject 0. The conclusion will stay the same no matter what
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