How many observations should be made if she wants to be 95.44 percent confident that the maximum error in the observed time is two seconds? Assume that the standard deviation of the task time is 6 seconds.
A)5
B)6
C)30
D)36
E)49

Question

Quizplus · Accepted Answer

We use the formula for the required sample size for estimating the population mean with a given margin of error and confidence level:
n = (z*sigma/E)^2
where:
z = the z-score corresponding to the desired confidence level (here, z = 1.96 for 95.44% confidence)
sigma = the population standard deviation (given as 6 seconds)
E = the maximum error allowed (here, E = 2 seconds)
Substituting these values, we get:
n = (1.96*6/2)^2 = 36.0584
This means that we need at least n = 37 observations (rounded up to the nearest integer) to achieve the desired level of precision. Therefore, the best choice is D.

How Many Observations Should Be Made If She Wants to Be