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 38 samples of water and determines the volume of Each sample. The 38 samples have a mean volume of $\bar { x } = 751.1 \mathrm {~mL} .$ . 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 $\sigma = 5.1$ Compute the value of the test statistic.
A) 3.00
B) 1.33
C) 0.18
D) 0.22

Question

Quizplus · Accepted Answer

The test statistic is calculated using the formula $z = \frac{{\bar{x} - \mu}}{{\sigma / \sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean, $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $z = \frac{{751.1 - 750}}{{5.1 / \sqrt{38}}}$ results in approximately 1.33.

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