A methods and measurement analyst wants to develop a time standard for a certain task. In a preliminary study, he observed one worker perform the task six times with an average observed time of 20 seconds and a standard deviation of two 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

A methods and measurement analyst wants to develop a time standard for a certain task. In a preliminary study, he observed one worker perform the task six times with an average observed time of 20 seconds and a standard deviation of two 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

Quizplus · Accepted Answer

To find the number of observations needed, use the formula for sample size in estimating a mean with a specified confidence level and margin of error: n = (Z * σ / E)^2. For 95.44% confidence, Z is approximately 2 (since 95.44% corresponds to 2 standard deviations in a normal distribution), σ is 2 seconds, and E is 1 second. Plugging in these values gives n = (2 * 2 / 1)^2 = 16.

A Methods and Measurement Analyst Wants to Develop a Time