Question

The company has a new process for manufacturing large artificial sapphires. In a trial run, 12 sapphires are produced. The mean weight for these 12 gems is x = 6.75 carats, and the sample standard deviation s = 0.33 carats. Find the 95% confidence interval for the population mean weight of artificial sapphires.

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 = 12 - 1 = 11

    =    =  _0.025,11 = 2.201

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

The margin of error is given by

E =  /2,d.f. * ( / n )

=  2.201 * (0.33 / 12)

= 0.2097

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

( - E ) <   <  ( + E)

(6.75  - 0.2097 )   <   <  (6.75  + 0.2097)

6.5403 <   < 6.9597

Required 95% confidence interval is (6.5403 , 6.9597)