How many observations should be made if she wants to be 0.8664 confident that the maximum error in the observed time is 0.5 second? Assume that the standard deviation of the task time is 4 seconds.
A)10
B)12
C)120
D)144
E)169

Question

Quizplus · Accepted Answer

The sample size required to achieve a desired level of confidence and maximum error in the observed time can be calculated using the formula:n = (Z^2 * s^2) / E^2where:n is the sample sizeZ is the z-score corresponding to the desired level of confidences is the standard deviation of the task timeE is the maximum error in the observed timeIn this case, we want to be 0.8664 confident that the maximum error in the observed time is 0.5 second, and the standard deviation of the task time is 4 seconds. Using a z-score table, we find that the z-score corresponding to a confidence level of 0.8664 is 1.5.Plugging these values into the formula, we get:n = (1.5^2 * 4^2) / 0.5^2 = 144Therefore, the correct answer is D) 144.

How Many Observations Should Be Made If She Wants to Be