At a water bottling facility, a technician is testing a bottle filling machine that is supposed to deliver 250 milliliters of water. The technician dispenses 50 samples of water and determines the volume of each sample. The 50 samples have a mean volume of $\bar { x } = 252.1 \mathrm {~mL}$. The machine is out of calibration if the mean volume differs from $250 \mathrm {~mL}$.
The technician wants to perform a hypothesis test to determine whether the machine is ou calibration. The standard deviation of the dispensed volume is known to be $\sigma = 6.4$. Comy value of the test statistic.
A) $0.30$
B) $2.32$
C) $5.87$
D) $0.33$

Question

Quizplus · Accepted Answer

The test statistic for this hypothesis test can be calculated using the formula $Z = \frac{{\bar{x} - \mu}}{{\sigma / \sqrt{n}}}$, where $\bar{x}$ is the sample mean, $\mu$ is the population mean (in this case, the target volume of 250 mL), $\sigma$ is the population standard deviation, and $n$ is the sample size. Plugging in the given values: $Z = \frac{{252.1 - 250}}{{6.4 / \sqrt{50}}}$ results in a test statistic of approximately 2.32.

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