Question

In a random sample of 32 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 61 ​months, with a standard deviation of 12 months. Construct and interpret a 90​% confidence interval for the mean length of sentencing for this crime.

We can be 90% confident that the mean length of sentencing for the crime is between ______ and ______ months.

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 61

sample standard deviation = s = 12

sample size = n = 32

Degrees of freedom = df = n - 1 = 31

At 90% confidence level the t is ,

= 1 - 90% = 1 - 0.90 = 0.10

/ 2 = 0.10 / 2 = 0.05

t _/2,df = t_0.05,31 = 1.696

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

= 1.696 * (12 / 32)

= 3.598

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

- E < < + E

61 - 3.598 < < 61 + 3.598

57.402 < < 64.598

We can be 90% confident that the mean length of sentencing for the crime is between 57.40 and 64.60 months.