Question

How much money do winners go home with from the television quiz show Jeopardy? To determine an answer, a random sample of winners was drawn and the amount of money each won was recorded and listed below. Estimate with 92% confidence the mean winning's for all the show's players.

34575 33181 18030 24597 29791

22710 34255 26599 30359 17544

32948 17259 20302 23942 28048

Upper confidence limit =

Lower confidence limit =

Answer 1

Solution:

Sample size = n = 15

df = n - 1 = 14

Using calculator , first we find the sample mean and sample SD.

= 26276

s = 6206.1325431268

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 =0.04

Also, d.f = n - 1 = 15 - 1 = 14

    =    =  _0.04,14 = 1.887

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

The margin of error is given by

E =  /2,d.f. * ( / n)

= 1.887 * (6206.1325431268 / 15)

= 3023.75999637

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

( - E ) <   <  ( + E)

(26276 - 3023.75999637)   <   <  (26276 + 3023.75999637)

23252.2400036 <   <  29299.7599964

Upper confidence limit = 29299.7599964 = 29300

Lower confidence limit = 23252.2400036 = 23252