During a time study,the following times were observed for a particular job using the continuous (non-snapback)method: 22,51,72,98,128,and 150 seconds.There is only one element per cycle.The sample standard deviation of the observed times has already been computed as 3.9 seconds.If an estimate for the average time that is within 4 percent of the true long-range average 95 percent of the time is desired,how many additional observations are needed?
A) Fewer than or equal to 40
B) Greater than 40 but fewer than or equal to 55
C) Greater than 55 but fewer than or equal to 70
D) Greater than 70

Question

Quizplus · Accepted Answer

To estimate the true long-range average with 95% confidence and within 4% margin of error, we need to use the formula n = (Zα/2 * σ/E)^2, where Zα/2 is the 1.96 for 95% confidence level, σ is the sample standard deviation, and E is the maximum error or margin of error (4% of the true average). Plugging in the given values, we get n = (1.96 * 3.9/0.04)^2 ≈ 67. Therefore, we need at least 67-6=61 additional observations (subtracting the 6 observations already made) to meet the desired criteria. Since 61 falls between 55 and 70, the best choice is C.

During a Time Study,the Following Times Were Observed for a Particular