Question

In a random sample of 39 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 57 ​months, with a standard deviation of 7 months. Construct a 95​% confidence interval for the mean length of sentencing for this crime.

the 95​% confidence interval is ​(?,?)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 57

Population standard deviation =    = 7

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 = Z_0.025 = 1.96

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

=1.96 * (7 /   39)

=2.1970
At 95% confidence interval estimate of the population mean
is,

- E < < + E

57​ - 2.1970 <   < 57​+ 2.1970

54.8030<   < 59.1970

( 54.8030 ,  59.1970 )