At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 1,000 milliliters of water. The technician dispenses 46 samples of water and determines the volume
Of each sample. The 46 samples have a mean volume of $\bar { x } = 1,000.9 \mathrm {~mL} .$ . The machine is out of Calibration if the mean volume differs from 1,000 mL.
The technician wants to perform a hypothesis test to determine whether the machine is out of calibration.
State the appropriate null and alternate hypotheses.

Question

At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 1,000 milliliters of water. The technician dispenses 46 samples of water and determines the volume
Of each sample. The 46 samples have a mean volume of $\bar { x } = 1,000.9 \mathrm {~mL} .$ . The machine is out of Calibration if the mean volume differs from 1,000 mL.
The technician wants to perform a hypothesis test to determine whether the machine is out of calibration.
State the appropriate null and alternate hypotheses. 
A) $H _ { 0 } : \mu = 1,000 , H _ { 1 } : \mu < 1,000$
B) $H _ { 0 } : \mu = 1,000.9 , H _ { 1 } : \mu > 1,000.9$
C) $H _ { 0 } : \mu = 1,000 , H _ { 1 } : \mu \neq 1,000$
D) $H _ { 0 } : \mu \neq 1,000.9 , H _ { 1 } : \mu = 1,000.9$

Quizplus · Accepted Answer

The null hypothesis ($H_0$) represents the scenario under which the machine is operating as expected, which is when the mean volume ($\mu$) is equal to 1,000 mL. The alternative hypothesis ($H_1$) should cover the possibility of the machine being out of calibration, which means the mean volume could be either less than or greater than 1,000 mL, hence $\mu \neq 1,000$.

At a Water Bottling Facility, a Technician Is Testing a Bottle