Confidence Intervals (Sample Size)

Question

You want to obtain a sample to estimate how much parents spend on their kid's birthday parties. Based on previous study, you believe the population standard deviation is approximately  dollars. You would like to be 95% confident that your estimate is within 5 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?

Answer 1

n = (z* * s/E)^2

where n = sample size

z* is critical z value computed as follows

first find critical probability = (1 + CL in decimal)/2 = (1 + 0.95)/2 = 0.975

then look up z* from table or by using statistical calculator = 1.96

E given as 5 and s given as 30.2 so:

n = (1.96 * 30.2/5)^2 = 140.15 ~ 141