Find the margin of error.
-To be able to say with 95% confidence level that the standard deviation of a data set is within 20% of the population's standard deviation, the number of observations within the data set must be greater than or equal to what quantity?
A)47
B)84
C)250
D)210

Question

Quizplus · Accepted Answer

The margin of error is 20% of the population's standard deviation. The sample size must be large enough to ensure that the sample standard deviation is within this margin of error with 95% confidence. The formula for the margin of error is:Margin of error = z * (standard deviation / sqrt(sample size))where z is the z-score corresponding to the desired confidence level. For a 95% confidence level, z = 1.96.We want the margin of error to be 20% of the population's standard deviation, so we can write:0.2 * population's standard deviation = 1.96 * (population's standard deviation / sqrt(sample size))Solving for sample size, we get:sample size = (1.96 / 0.2)^2 = 96.04Therefore, the number of observations within the data set must be greater than or equal to 97.

Find the Margin of Error