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 σ=69.2σ=69.2 dollars. You would like to be 99% confident that your estimate is within 1.5 dollar(s) of average spending on the birthday parties. How many parents do you have to sample?

Answer 1

Solution :

Given that,

standard deviation = = 69.2

margin of error = E = 1.5

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z_/2 = Z_0.005 = 2.576

Sample size = n = ((Z_/2 * ) / E)²

= ((2.576 * 69.2 ) / 1.5)²

= 14122.88

= 114123

Sample size = 14123