Question

In a random sample of 39 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 66

​months, with a standard deviation of 14 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 = = 66

sample standard deviation = s = 14

sample size = n = 39

Degrees of freedom = df = n - 1 = 39 -1 = 38

At 95% confidence level

= 1-0.95% =1-0.95 =0.05

/2 =0.05/ 2= 0.025

t/2,df = t0.025,99 = 3.50

t /2,df = 2.02

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

=2.02 * (14 / 39)

Margin of error = E = 4.54

The 95% confidence interval estimate of the population mean is,

- E < <  + E

66 -4.54 < < 66 + 4.54

61.46 < < 70.54

(61.46,70.54)

A 95​%confidence interval for the mean length of sentencing for this crime is (61.46,70.54)