Question

In a random sample of 39 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 53 ​months, with a standard deviation of 8 months. Construct and interpret a 90​% confidence interval for the mean length of sentencing for this crime.

Answer 1

Solution :

Given that,

= 53

s = 8

n =39

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

At 90% confidence level the z is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,38 = 1.686

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

= 1.686 * (8 / 39)

= 2.1

Margin of error = 2.1

The 90% confidence interval estimate of the population mean is,

- E < < + E

53 - 2.1 < 53+ 2.1

50.9 < < 55.1

(50,9, 55.1 )