Question

In a random sample of 39 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 55 ​months, with a standard deviation of 15 months. Construct and interpret a 95​% confidence interval for the mean length of sentencing for this crime.

Answer 1

Solution :

Given that,

Point estimate = sample mean =     = 55

Population standard deviation =    = 15

Sample size n =39

At 95% confidence level the z is ,

= 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

Z/2 = Z0.025 = 1.96   ( Using z table )

Margin of error = E =   Z/2    * ( /n)
= 1.96 * (15 / 39 )

= 4.7078
At 95% confidence interval estimate of the population mean
is,

- E < < + E

55 -4.7078 <   < 55+ 4.7078

50.2922 <   < 59.7078

( 50.2922 , 59.7078 )