A methods and measurements analyst needs to develop a time standard for a certain task. In a preliminary study, he observed one of his workers perform this task five times, with the following results: $$\begin{array} { | l | c | c | c | c | c | }
\hline \text { Observation } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Time(Seconds) } & 84 & 76 & 80 & 84 & 76 \
\hline
\end{array}$$ How many observations should be made if the analyst wants to be 99.74 percent confident that the maximum error in the observed time is two seconds? Assume that the standard deviation of the task time is four seconds.
A) 5
B) 6
C) 25
D) 36
E) 49

Question

A methods and measurements analyst needs to develop a time standard for a certain task. In a preliminary study, he observed one of his workers perform this task five times, with the following results: $$\begin{array} { | l | c | c | c | c | c | } 
\hline \text { Observation } & 1 & 2 & 3 & 4 & 5 \
\hline \text { Time(Seconds) } & 84 & 76 & 80 & 84 & 76 \
\hline
\end{array}$$ How many observations should be made if the analyst wants to be 99.74 percent confident that the maximum error in the observed time is two seconds? Assume that the standard deviation of the task time is four seconds.
A) 5
B) 6
C) 25
D) 36
E) 49

Quizplus · Accepted Answer

The sample size needed to be 99.74 percent confident that the maximum error in the observed time is two seconds can be calculated using the formula:n = (Z^2 * s^2) / E^2where:n is the sample sizeZ is the z-score for the desired confidence levels is the standard deviation of the task timeE is the maximum errorIn this case, the confidence level is 99.74 percent, which corresponds to a z-score of 3.0. The standard deviation of the task time is four seconds, and the maximum error is two seconds. Plugging these values into the formula, we get:n = (3.0^2 * 4^2) / 2^2 = 36Therefore, the analyst should make 36 observations to be 99.74 percent confident that the maximum error in the observed time is two seconds.

A Methods and Measurements Analyst Needs to Develop a Time