In a random sample of 40 felons convicted of aggravated assa

In a random sample of 40 felons convicted of aggravated assault, it was determined that the mean length of sentencing was 54 months, with a standard deviation of 8 months. Construct and interpret a 95% confidence interval for the mean length of sentence for an aggravated assault conviction.

Solution

alpha = 0.05

alpha / 2 = 0.025

df = 39

T = 2.021

interval

54 +/- 2.021 * 8 / srqt(40)

54 +/- 2.556

51.444 , 56.556

we are 95% confident that the mean length of sentence for an aggravated assault conviction is between 51.444 and 56.556