2
(Observed

Expected)
2
 
Expected
Chi Square

Goodness of Fit Test
Objective: Define the chi-square
goodness of fit test and explain the
three conditions necessary to its proper
use and the purpose of using it.
Hockey players' birth months from
Gladwell (2008)
Chi Square
H0 :
HA :
All Quarters of the Year produce the same number
of Hockey Players
Some Quarters of the Year DO NOT produce the same
number of Hockey Players
  15
P Value  .0018
2
Students Passing AP Statistics by Art
Strand
Total Students
TOTALS
Art Strand
Observed
Value
24
Music
18
14
Visual Arts
9
12
Theatre
6
10
Dance
3
60
36
Expected Value
Students Passing AP Statistics by Art
Strand
Total Students
TOTALS
Art Strand
Observed
Value
24
Music
18
14.4
14
Visual Arts
9
8.4
12
Theatre
6
7.2
10
Dance
3
6
36
36
60
Expected Value
✔Check Conditions
• Random (Simple Random Sample)
• Independence (10% condition)
• Large Counts (Expected Values =>5)
Hypotheses
• H0: All proportions (of each strand) are equal
• HA: At least two of the proportions are NOT equal
  .05

Chi Test Statistic
2
2
2
2
(18
14.4)
(9

8.4)
(6

7.2)
(3

6)
2 



14.4
8.4
7.2
6



Chi Test Statistic
2
2
2
2
(18
14.4)
(9

8.4)
(6

7.2)
(3

6)
2 



14.4
8.4
7.2
6
2  .9  .043  .2 1.5
2  2.64