A Methods and Measurement Analyst wants to develop a time standard for a certain task.In a preliminary study,he observed one employee perform the task six times with an average of 20 seconds and a standard deviation of 2 seconds. How many observations should be made if he wants to be 95.44 percent confident that the maximum error in the observed time is one second?
A)3
B)4
C)13.3
D)16
E)25

Question

Quizplus · Accepted Answer

To achieve a 95.44% confidence level with a maximum error of one second, the analyst needs to use the formula for the sample size in estimating a mean with a specified precision: $n = \left(\frac{Z\sigma}{E}\right)^2$, where $Z$ is the Z-value corresponding to the desired confidence level (for 95.44%, $Z = 2$), $\sigma$ is the standard deviation (2 seconds), and $E$ is the maximum error allowed (1 second). Plugging in the values: $n = \left(\frac{2*2}{1}\right)^2 = 16$.

A Methods and Measurement Analyst Wants to Develop a Time