At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 500 milliliters of water. The technician dispenses 38 samples of water and determines the volume of each sample. The 38 samples have a mean volume of $\bar { x } = 497.7 \mathrm {~mL}$ . The machine is out of calibration if the mean volume differs from 500 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 $\sigma = 5.1$
i). State the appropriate null and alternate hypotheses.
ii). Compute the value of the test statistic.
iii). State a conclusion. Use the $\alpha = 0.05$ level of significance.

Question

At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 500 milliliters of water. The technician dispenses 38 samples of water and determines the volume of each sample. The 38 samples have a mean volume of $\bar { x } = 497.7 \mathrm {~mL}$ . The machine is out of calibration if the mean volume differs from 500 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 $\sigma = 5.1$ 
i). State the appropriate null and alternate hypotheses.
ii). Compute the value of the test statistic.
iii). State a conclusion. Use the $\alpha = 0.05$ level of significance.

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The Answer of At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 500 milliliters of water. The technician dispenses 38 samples of water and determines the volume of each sample. The 38 samples have a mean volume of $\bar { x } = 497.7 \mathrm {~mL}$ . The machine is out of calibration if the mean volume differs from 500 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 $\sigma = 5.1$ 
i). State the appropriate null and alternate hypotheses.
ii). Compute the value of the test statistic.
iii). State a conclusion. Use the $\alpha = 0.05$ level of significance.

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