Question

A large sample of data (n = 335) from a Calgary observatory produced a mean daily counting rate for cosmic rays of 3465.46, and a standard deviation of 127.72. Use these sample data and construct a 90% confidence interval for the mean of the daily counting rates.

Answer 1

Solution:

Given that,

n = 335

=   3465.46

s = 127.72

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

Our aim is to construct 90% confidence interval.   

c = 0.90

= 1- c = 1- 0.90 = 0.10

  /2 = 0.10 2 = 0.05

Also, d.f = n - 1 = 335 - 1 = 334   

    =    =  _0.05,334 = 1.649

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

The margin of error is given by

E =  /2,d.f. * (s / n)

= 1.649 * (127.72/ 335)

= 11.51

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

( - E ) <   <  ( + E)

(3465.46 - 11.51)   <   <  (3465.46 + 11.51)

3453.95 <   <  3476.97

Required 90% confidence interval is (3453.95 , 3476.97)