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 (z = 1.96)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 determine the number of additional observations needed, we can use the formula:

n = [z*(sigma/x)]^2

where:
n = sample size
z = z-score for the desired confidence level (1.96 for 95% confidence)
sigma = sample standard deviation
x = desired margin of error as a decimal (0.04 for 4%)

Plugging in the given values, we get:

n = [1.96*(3.9/x)]^2
n = [1.96*(3.9/0.04)]^2
n = 55.13

Since we cannot have a partial observation, we round up to the nearest whole number and get a sample size of 56. Therefore, the best choice is C, since it falls within the range of 56 observations.

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