If a researcher wants a 99.7% level of confidence (Z-Value = 3.00) and has determined the acceptable precision width to be 90, the sampling error on either side of the mean would be
A) 27
B) 30
C) 90
D) 270

Question

Quizplus · Accepted Answer

The formula for margin of error (sampling error) is

Margin of Error = Z-value * (Standard Deviation / Square root of sample size)

Since the level of confidence (Z-value) is 3.00, we can plug in the values and solve for the standard deviation.

3.00 = (X - mean) / standard deviation
3.00 * standard deviation = X - mean
standard deviation = (X - mean) / 3.00

Now we can plug in the standard deviation value into the margin of error formula and solve for the sample size.

90 = 3.00 * (standard deviation / square root of sample size)
30 = standard deviation / square root of sample size
900 = standard deviation^2
standard deviation = 30 * square root of 10

Plugging the standard deviation into the margin of error formula gives us:

Margin of Error = 3.00 * (30 * square root of 10 / square root of sample size)

We want a margin of error of 90, so we can solve for the sample size:

90 = 3.00 * (30 * square root of 10 / square root of sample size)
30 = 30 * square root of 10 / square root of sample size
square root of sample size = square root of 10
sample size = 10

So the sampling error on either side of the mean would be:

Margin of Error = 3.00 * (30 * square root of 10 / square root of 10) = 90.

Therefore, the correct choice is B.

If a Researcher Wants a 99