Question

28 randomly selected students took the calculus final. If the sample mean was 87 and the standard deviation was 11.7. construct a 92% confidence interval for the mean score students.

Answer 1

Solution =

Given that,

n = 28

   = 87

s = 11.7  

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

Our aim is to construct 92% confidence interval.   

c = 0.92

= 1 - c = 1 - 0.92 = 0.08

  /2 = 0.08 2 = 0.04

Also, d.f = n - 1 = 27

    =    =  0.04,27 = 1.819

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

The margin of error is given by

E =  /2,d.f. * ( / n )

= 1.819 * ( 11.7/ 28 )

= 4.022

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

( - E ) <   <  ( + E)

( 87 - 4.022 )   <   <  ( 87 + 4.022 )

82.978 <   < 91.022

Required.99% confidence interval is ( 82.978 , 91.022 )