Question

In a random sample of

39

criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was

61

​months, with a standard deviation of

14

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,

= 61

s = 14

n = 39

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

At 95% confidence level the t is ,

  = 1 - 95% = 1 - 0.95 = 0.05

/ 2 = 0.05 / 2 = 0.025

t _/2,df = t_0.025,38 = 2.024

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

= 2.024 * (14 / 39 )

= 4.54

Margin of error = 4.54

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

- E < < + E

61 - 4.54 < < 61 + 4.54

56.46 < < 61.54

( 56.46, 61.54 )