Question

a. The following are the GPA's of a class of Stats students: 3.4, 3.1, 2.0, 2.3, 3.3, 2.6, 1.8, 0.2, 3.1, 4.0, 0.7, 2.3, Construct the 99% CI.

b.Would a 90% CI be larger or smaller?

Answer 1

Solution:

a)

3.4, 3.1, 2.0, 2.3, 3.3, 2.6, 1.8, 0.2, 3.1, 4.0

Sample size n = 10

Using calculator

sample mean = 2.58

Sample standard deviation s = 1.0768266135064

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

Our aim is to construct 99% confidence interval.   

c = 0.99

= 1 - c = 1 - 0.99 = 0.01

  /2 = 0.01 2 = 0.005

Also, d.f = n - 1 = 10 - 1 = 9

    =    =  _0.005,9 = 3.250

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

The margin of error is given by

E =  /2,d.f. * ( / n )

= 3.250 * (1.0768266135064 / 10)

= 1.1067

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

( - E ) <   <  ( + E)

(2.58 - 1.1067)   <   <  (2.58 + 1.1067)

1.4733 <   < 3.6867

Required.99% confidence interval is (1.4733 , 3.6867)

b)

Smaller

Because as confidence level decreases , margin of error decreases and interval becomes smalller.