Question

A random sample of n = 41 articles yielded a mean Flesch-Kincaid grade level of X = 11.67. We assumed the population standard deviation was σ = 1.865.

Compute a 99.7% confidence interval for the unknown parameter, based on the study. Show work.

Answer 1

Solution :

Given that,

Z$\alpha$/2 = Z_0.0015 = 2.968

Margin of error = E = Z$\alpha$/2 * ( $\sigma$ /$\sqrt$n)

= 2.968 * ( 1.865 /  $\sqrt$41 )

= 0.86

At 99.7% confidence interval estimate of the population mean is,

  ± E   

T

= 11.67  ± 0.86

= ( 10.81, 12.53 )