Question

In a random sample of

39

criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was

56

​months, with a standard deviation of

12

months. Construct and interpret a 95​%

confidence interval for the mean length of sentencing for this crime.

Answer 1

Solution :

Given that,

= 56

=

n = 39

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 = 1.96

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

= 1.96* ( 12/ 39)

= 3.766

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

- E < < + E

56-3.766< < 56+3.766

52.234< < 59.766

52.234 , 59.766