Question

You are starting an Internet Service Provider (ISP) and need to estimate the average internet usage of households in one week for your business plan and model. How many households should you randomly select to be 87% confident your estimate is within a margin of error of 15 minutes? Assume we know the population standard deviation is σ = 56 minutes.   rounded to the nearest hundredth is

You need to sample how many households to be 87% confident that your estimate is within 15 minutes of the true population mean internet usage?

Answer 1

Solution :

Given that,

Population standard deviation = = 56

Margin of error = E = 15

At 87% confidence level the z is,

= 1 - 87%

= 1 - 0.87 = 0.13

/2 = 0.065

Z_/2 = Z_0.065 = 1.514

sample size = n = [Z_/2* / E] ²

n = [ 1.514 * 56 / 15 ]²

n = 31.95

Sample size = n = 32