Question

A sample of 75 concrete blocks had a mean mass of 38.3 kg with a standard deviation of 0.4 kg.

Find a 95% confidence interval for the mean mass of this type of concrete block. (Round the final answers to three decimal places.)

The 95% confidence interval is

Answer 1

Solution:

Note that, Population standard deviation() is unknown. So we use t distribution.

Our aim is to construct 95% confidence interval.

c = 0.95

= 1- c = 1- 0.95 = 0.05

  /2 = 0.05 2 = 0.025

Also, d.f = n - 1 = 75 - 1 = 74

    =    =  _0.025,74 = 1.993

( use t table or t calculator to find this value..)

The margin of error is given by

E =  /2,d.f. * ( / n )

= 1.993 * (0.4 / 75)

= 0.09205272691

Now , confidence interval for mean() is given by:

( - E ) <   <  ( + E)

(38.3 - 0.09205272691)   <   <  (38.3 + 0.09205272691)

38.208 <   <  38.392

The 95% confidence interval is (38.208 , 38.392)