Question

A researcher specializing in the area of juvenile delinquency is interested in estimating the average age when delinquency first begins. Taking a random sample of 57 juveniles, she determines a sample mean of 13.4 years and a sample standard deviation of 1.5 years. Construct a 99% confidence interval to estimate when the average population (mean) age of delinquency begins

Answer 1

solution

Given that,

= 13.4

s = 1.5

n = 57

Degrees of freedom = df = n - 1 = 57- 1 = 56

At 99% confidence level the t is ,

= 1 - 99% = 1 - 0.99 = 0.01

/ 2 = 0.01 / 2 = 0.005

t /2  df = t0.005, 56= 2.667    ( using student t table)

Margin of error = E = t/2,df * (s /n)

= 2.667* ( 1.5/ 57) = 0.5299

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

- E < < + E

13.4  -0.5299 < < 13.4 + 0.5299

12.8701 < < 13.9299

(12.8701 ,13.9299 )