A methods and measurements analyst for Digital Devices needs to develop a time standard for the task of assembling a computer mouse. In a preliminary study, she observed one of her workers perform this task six times with the following results: $$\begin{array} { l r r r r r r }
\text { Observation } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Time (seconds) } & 46 & 38 & 40 & 34 & 42 & 40
\end{array}$$ How many observations should be made if she wants to be 86.64 percent confident that the maximum error in the observed time is .5 second? Assume that the standard deviation of the task time is four seconds.
A) 10
B) 12
C) 120
D) 144
E) 169

Question

A methods and measurements analyst for Digital Devices needs to develop a time standard for the task of assembling a computer mouse. In a preliminary study, she observed one of her workers perform this task six times with the following results: $$\begin{array} { l r r r r r r } 
\text { Observation } & 1 & 2 & 3 & 4 & 5 & 6 \
\hline \text { Time (seconds) } & 46 & 38 & 40 & 34 & 42 & 40
\end{array}$$ How many observations should be made if she wants to be 86.64 percent confident that the maximum error in the observed time is .5 second? Assume that the standard deviation of the task time is four seconds.
A) 10
B) 12
C) 120
D) 144
E) 169

Quizplus · Accepted Answer

To determine the sample size required for the study, we use the following formula:

$n = (\dfrac{z\sigma}{E})^2$

Where: 
$n$ = sample size 
$z$ = z-value for desired confidence level (86.64 percent = 1.5 standard deviations, approximately) 
$\sigma$ = standard deviation of the task time (given as 4 seconds)
$E$ = maximum error in observed time (given as 0.5 seconds)

Substituting the given values, we get:

$n = (\dfrac{(1.5)(4)}{0.5})^2 = 144$

Therefore, the analyst should make 144 observations to be 86.64 percent confident that the maximum error in the observed time is 0.5 second.

The correct answer is (D) 144.

A Methods and Measurements Analyst for Digital Devices Needs to Develop