Question

(a)	The following data shows the number of hours that 8 hospital patients slept following the administration of a certain anesthetic. 8, 5, 12, 10, 11, 4, 6, 10, Find a 95% confidence interval for the average hours slept following the administration of the anesthetic for the sampled population.

Answer 1

Solution:

We have a sample of size n = 8

8, 5, 12, 10, 11, 4, 6, 10

Using this, first we find sample mean() and sample standard deviation(s).

=   

= (8+ 5+ .......+ 10)/8

=   8.25

To find the sample standard deviation s , we need to prepare a table.

	x	x2
	8	64
	5	25
	12	144
	10	100
	11	121
	4	16
	6	36
	10	100
Sum	66	606

Now ,

Sample variance s² =

= [1/(8 - 1])[606 - (66²/8) ]

= 8.7857142857143

Now ,

s = variance = 8.7857142857143  = 2.9641

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 = 8 - 1 = 7

    =    =  _0.025,7 = 2.365

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

The margin of error is given by

E =  /2,d.f. * ( / n )

= 2.365  * (2.9641 / 8 )

= 2.4784

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

( - E ) <   <  ( + E)

(8.25 - 2.4784)   <   <  (8.25 + 2.4784)

5.7716 <   < 10.7284

Required 95% confidence interval is (5.7716 , 10.7284)