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)3
B)4
C)13.3
D)16
E)25

Question

Quizplus · Accepted Answer

The formula to calculate the sample size for estimating the population mean, with a specified level of confidence and margin of error is:
n = (Z^2 * σ^2) / E^2
Where, Z is the critical value for the level of confidence (in this case 95.44% confidence corresponds to a Z-value of 1.96), σ is the population standard deviation (unknown), and E is the maximum error or margin of error (1 second).
Assuming the worst-case scenario where σ = 0.5 (maximum possible standard deviation for time observations), we can substitute the values in the formula and get:
n = (1.96^2 * 0.5^2) / 1^2
n = 3.8416
Rounding up to the next integer, we get the minimum sample size required as 4. Therefore, the best choice is option D.

How Many Observations Should Be Made If He Wants to Be