Question

The grades of 5 randomly selected students in Engineering Statistics are shown below. Construct a 95% two-sided confidence interval for the true mean of student grades?

Students	1	2	3	4	5
Grades	95	85	65	75	80

Answer 1

Solution:

Given a sample of size n = 5

95,85,65,75,80

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

Use calculator.

= 80

s = 11.180339887499

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 = 5 - 1 = 4

    =    =  _0.025,4 = 2.776

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

The margin of error is given by

E =  /2,d.f. * ( / n )

= 2.776 * (11.180339887499 / 5)

= 13.88

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

( - E ) <   <  ( + E)

(80 - 13.88)   <   <  (80 + 13.88)

66.12 <   < 93.88

Required 95% confidence interval is (66.12 , 93.88)