Given a level of confidence of 95% and a population standard deviation of 14, answer the following:
(A) What other information is necessary to find the sample size (n)?
(B) Find the Maximum Error of Estimate (E) if n = 78.
(A) To find the sample size (n) given a level of confidence and a population standard deviation, you would also need the desired margin of error (E) and the level of confidence interval (Z-value). The margin of error indicates the maximum amount of error you are willing to tolerate in your estimate, while the Z-value corresponds to a specific level of confidence. With these three pieces of information, you can calculate the sample size (n) using the following formula:
n = ((Z * σ) / E)^2
Where:
n = sample size
Z = Z-value at the desired level of confidence
σ = population standard deviation
E = margin of error
(B) To find the Maximum Error of Estimate (E) if the sample size (n) is 78, you would need the formula rearranged to calculate E. Rearranging the formula, we get:
E = (Z * σ) / √n
Given that n = 78, you would also need the Z-value at the desired level of confidence and the population standard deviation (σ) to substitute into the formula in order to calculate the Maximum Error of Estimate (E).