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

question 33

Essay

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 39 samples of water and determines the volume of each sample. The 39 samples have a mean volume of $\bar { x } = 498.3 \mathrm {~mL}$ . The machine is out of calibration if the mean volume differs from $500 \mathrm {~mL}$ .

The technician wants to perform a hypothesis test to determine whether the machi out of calibration. The standard deviation of the dispensed volume is known to be
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. s

---

Definitions:

Easy Entry And Exit

A characteristic of competitive markets where there are minimal barriers for new firms to enter or exit the market.

Perfect Competition

A theoretical market structure that features no barriers to entry, a large number of sellers and buyers, completely homogenous products, and perfect information available to all market participants.

Chronic Excess Capacity

A situation where industries consistently operate below their full output capacity due to prolonged demand shortfall.

Monopolistic Competition

A market structure characterized by many firms selling products that are similar but not identical, allowing for competition based on price, quality, and marketing.