How many parents do you have to sample?n =

Question

You want to obtain a sample to estimate how much parents spend on their kids birthday parties. Based on previous study, you believe the population standard deviation is approximately  dollars. You would like to be 90% confident that your estimate is within 10 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?n = 

Answer 1

90% confidence is equivalent to 1.644854 standard deviations. So you want $10 = 1.644854 σ. That tells us the standard deviation of the sample mean needs to be 6.079567.

The standard deviation of the sample mean is equal to 79.8 / sqrt(n - 1) where n is the sample size.

79.8 / sqrt(n - 1) = 6.079567

79.8 / 6.079567 = sqrt(n - 1)

(79.8 / 6.079567)^2 + 1 = n = 173.3

But you can't sample .3 of a person, so round up to 174.