How many observations should be made if he wants to be 95.44 percent confident that the maximum error in the observed time is one second?
A)64
B)86
C)100
D)144
E)169

Question

Quizplus · Accepted Answer

The formula for finding the sample size required for a given maximum error and level of confidence is:

n = (z^2 * s^2) / E^2

where:
z = the z-score corresponding to the desired level of confidence (1.96 for 95.44% confidence)
s = the standard deviation of the population (unknown in this case, so we'll use a conservative estimate of 0.5, which maximizes the sample size)
E = the maximum error (1 second in this case)

Plugging in these values, we get:

n = (1.96^2 * 0.5^2) / 1^2
n = 3.8416 / 1
n = 3,841.6

We always round up to the nearest whole number of observations (you can't have a fraction of an observation), so:

n = 3,842

Therefore, the best choice is C, with 100 observations.

How Many Observations Should Be Made If He Wants to Be