Question

If n=30, ¯xx¯(x-bar)=48, and s=3, find the margin of error at a 90% confidence level

Give your answer to two decimal places.

Answer 1

Solution:

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

Confidence level = 90%

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05

Also, d.f = n - 1 = 30 - 1= 29  

    =    =  _0.05,29 = 1.699

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

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.699 * (3 / 30)

= 0.93

margin of error = 0.93