Question

A random sample of stock prices per share (in dollars) is shown. Find the 92% confidence interval for the mean stock price. Assume the population of stock prices is normally distributed.

26.6
75.37
3.81
28.37
40.25
13.88
53.8
28.25
10.87
12.25

Answer 1

Solution =

We are given a data of sample size n = 10

26.6,75.37,3.81,28.37,40.25,13.88,53.8,28.25,10.87,12.25

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

=   

= (26.6 + 75.37.......+ 12.25)/10

= 29.35

Now ,

s=   

Using given data, find Xi - for each term.Take square for each.Then we can easily find s.

s = 22.03

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 = 9

    =    =  0.04,9 = 1.973

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

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.973 * ( 22.03/ 10 )

= 13.742

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

( - E ) <   <  ( + E)

( 29.35 - 13.742 )   <   <  ( 29.35 + 13.742 )

15.608 <   < 43.092

Required 92% Confidence interval is ( 15.608 , 43.092 )