Question

Given the following Data Set for a Sample, build a 83% CI=(a, b) for the Average.

X={1.2, 3.7, 1.9, 2.3, 2.7, 2.9, 3.4, 1.7, 0.9}

a. CI=(1.81, 2.78)

b. None

c. CI=(1.86,2.74)

d. CI=(2, 3)

Answer 1

Solution:

n = 9

1.2, 3.7, 1.9, 2.3, 2.7, 2.9, 3.4, 1.7, 0.9

Using calculator ,

= 2.3

s = 0.96046863561493

Our aim is to construct 90% confidence interval.   

c = 0.83

= 1- c = 1- 0.83 = 0.17

  /2 = 0.085

Also, d.f = n - 1 = 9 - 1 = 8

    =    =  _0.085,8 = 1.508

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

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.508 * (0.96046863561493 / 9)

= 0.48

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

( - E ) <   <  ( + E)

(2.3 - 0.48)   <   <  (2.3 + 0.48)

1.81 <   < 2.78

Required 83% confidence interval is

(1.81 , 2.78 )