Question

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.

Answer 1

Sure! The quality-control inspector can use a t-test to check if the machine that fills the grapefruit juice bottles is working properly.

The inspector compares the average amount of juice in the bottles (179.6 ml) to the target amount (180 ml). Using a t-test formula, the inspector calculates a t-value of -1.94.

Because -1.94 falls within the range of -2.022 to 2.022 for a 5% level of significance, the inspector can't reject the idea that the machine is filling the bottles correctly.

Therefore, based on the sample, there's not enough evidence to say the machine isn't working properly, and the average amount of liquid in the bottles is not significantly different from 180 ml.