Question

Assume that a sample is used to estimate a population mean μμ. Find the 99% confidence interval for a sample of size 643 with a mean of 17.6 and a standard deviation of 17.5. Enter your answer accurate to one decimal place (because the sample statistics are reported accurate to one decimal place).

<μ<<μ<

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 17.6

Population standard deviation =    = 17.5

Sample size = n =643

At 99% confidence level the z is ,

  = 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

Z/2 = Z0.005 = 2.576   ( Using z table )

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

= 2.576 * (17.5 / 643)

E= 1.8

At 99% confidence interval estimate of the population mean is,

- E < < + E

17.6-1.8 < < 17.6+1.8

15.8< < 19.4