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? The standard deviation of task times is 6 seconds.
A) 5
B) 6
C) 30
D) 36
E) 49

Question

Quizplus · Accepted Answer

Using the formula for determining sample size for a population mean with known standard deviation and a desired level of confidence:

$n = \left(\frac{z\sigma}{E}ight)^2$

where:
z = the z-score for the desired level of confidence (in this case, 1.96 for 95.44% confidence)
$\sigma$ = the standard deviation of task times (6 seconds)
E = the maximum allowable error in the observed time (2 seconds)

Substituting these values, we get:

$n = \left(\frac{1.96	imes6}{2}ight)^2 = 36.0576$

Rounding up, we get a sample size of 36. Therefore, the best choice is D) 36.

How Many Observations Should Be Made If She Wants to Be