Yi is running for class president. To try to predict how people will vote, she wants to take a poll with a 90% confidence level (z*-score of 1.645) and an estimated margin of error of 4%. What is the approximate minimum sample size for Yi’s initial poll?
Accepted Solution
A:
90The information that you'd need in determining sample size when the standard deviation is unknown is:
z-value for the given level of confidence ⇒ The level of confidence is 90% and the z-value by convention is 1.645
The margin error (E) = 4%
The proportion of the population that you'd expect to vote for Yi. If this information isn't provided, use 50%. We call this value, p, the probability of success.
The probability of not success is q = 1 - 0.5 = 0.5
STEP 1: Half the margin error = 0.04 ÷ 2 = 0.02
STEP 2: Multiply the probability of success by the probability of fail = 0.5 × 0.5 = 0.25
STEP 3: Divide z-score by half of E = 1.645 ÷ 0.02 = 82.25 Then square the answer = 82.25² = 6765 rounded to the nearest integer)
STEP 4: Multiply the answer from STEP 2 by the answer from STEP 4 0.25 × 6765 = 1691 (rounded to the nearest integer)