Consider the following to answer the question(s) below:
The Dispenser Right Company makes a soft drink dispensing machine used in many fast food restaurants. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by a particular machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed:

-In order to be 99% accurate to within 0.02 ounces, what sample size would be needed if the sample standard deviation is 0.18?
A) 538
B) 23
C) 11
D) 1159
E) 440

Question

Consider the following to answer the question(s) below:
The Dispenser Right Company makes a soft drink dispensing machine used in many fast food restaurants. When the machine is running properly, the average number of fluid ounces in the cup should be 14. Periodically the machines need to be tested to make sure that they have not gone out of adjustment. To do this, six cups are filled by a particular machine and a technician carefully measures the volume in each cup. In one such test, the following data were observed:
 
-In order to be 99% accurate to within 0.02 ounces, what sample size would be needed if the sample standard deviation is 0.18?
A) 538 
B) 23 
C) 11 
D) 1159 
E) 440

Quizplus · Accepted Answer

To determine the sample size needed for a specific level of accuracy, we use the formula for the sample size in estimating a population mean with a certain confidence level: $n = \left(\frac{Z \cdot \sigma}{E}\right)^2$, where $n$ is the sample size, $Z$ is the Z-score corresponding to the desired confidence level (for 99% confidence, $Z \approx 2.576$), $\sigma$ is the population standard deviation (0.18 in this case), and $E$ is the margin of error (0.02 in this case). Plugging in the values: $n = \left(\frac{2.576 \cdot 0.18}{0.02}\right)^2 \approx 538$.

Consider the Following to Answer the Question(s) Below