Question

In a random sample of 38 criminals convicted of a certain​ crime, it was determined that the mean length of sentencing was 63 ​months, with a standard deviation of 5 months. Construct a 90​% confidence interval for the mean length of sentencing for this crime.

The 90​% confidence interval is ????

(use ascending order)

Answer 1

Solution :

Given that,

Point estimate = sample mean = = 63

Population standard deviation =    = 5
Sample size = n =38

At 90% confidence level the z is

= 1 - 90% = 1 - 0.90 = 0.1

/ 2 = 0.1 / 2 = 0.05

Z/2 = Z0.05 = 1.645 ( Using z table )

Margin of error = E = Z/2    * ( /n)

= 1.645* ( 5/  38 )

= 1.33
At 90% confidence interval mean
is,

- E < < + E

63 - 1.33 <   < 63 + 1.33

61.67 <   < 64.33