Question

Suppose you are trying to estimate the population mean for the number of Denver people that will vote in the next election. You know there are 800,000 voters in Denver. You have sampled 41,000 Denver citizens and have calculated a sample mean of 150,000 likely voters in the next election. You believe the population standard deviation to be 80,000 voters. Please calculate a confidence interval for your sample mean, assuming you wish to be 95% confident.  

Answer 1

Solution :

Given that,

= 150,000

= 80,000

n = 41,000

At 95% confidence level the z is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z_/2 = Z_0.025 = 1.960

Margin of error = E = Z_/2* (/n)

= 1.960 * (80,000 / 41,000  )

= 774.38

At 95% confidence interval estimate of the population mean is,

- E < < + E

150,000 - 774.38 < < 150,000 + 774.38

149225.62 < < 150774.38

(149000 , 151000)