At a water bottling facility, a technician is testing a bottle filling machine that is

supposed to deliver 750 milliliters of water. The technician dispenses 42 samples

of water and determines the volume of each sample. The 42 samples have a mean

volume of x = 747.7 mL. The machine is out of calibration if the mean volume

differs from 750 mL.

The technician wants to perform a hypothesis test to determine whether the

machine is out of calibration. The standard deviation of the dispensed volume is

known to be = 6.1.

i). State the appropriate null and alternate hypotheses.

ii). Compute the value of the test statistic.

iii). State a conclusion. Use the = 0.01 level of significance.