2.13. GOODNESS-OF-FIT TEST:
2
TEST 93
Table 2.13: e calculation results for the goodness-of-fit test
Non-Overlapping Interval
o
j
e
j
(o
j
– e
j
)
2
e
j
Lower range x
j-L
Upper range x
j-U
-∞ 49.7 2 2.338724 0.049058
49.7 52.3 4 4.481793 0.051793
52.3 54.9 9 9.282114 0.008574
54.9 57.5 15 15.06146 0.000251
57.5 60.2 18 19.14866 0.068903
60.2 62.8 22 19.07542 0.448386
62.8 65.4 14 14.88931 0.053116
65.4 68.0 9 9.105954 0.001233
68.0 70.6 4 4.363151 0.030226
70.6 +∞ 3 2.253421 0.247348
W =
(o
j
– e
j
)
2
e
j
0.958889
10
j = 1
culated with the function in Microsoft Excel as:
e
2
D N P
.
x
2L
X x
2U
/
D N
Œ
F
.
x
2U
/
F
.
x
2L
/
D 100
Œ
NORM:DIST
.
52:3; 60:1; 5:23; TRUE
/
NORM:DIST
.
49:7; 60:1; 5:23; TRUE
/
D 4:481793:
• Step 5: e test statistic W .
e test statistic W can be calculated per Equation (2.129). In the above table, the last
column is the values of
.
o
j
e
j
/
2
e
j
in each non-overlapping interval. According to the above
table, we have the test statistic
W D 0:959:
• Step 6: Select a significant level a D 0:05.
• Step 7: W
critical
D
2
1a
.k/.
By Equations (2.132) or (2.133) or the Chi-square Table 2.11:
W
critical
D
2
1a
.
k
/
D
2
10:05
.
10 2 1
/
D
2
0:95
.
7
/
D 14:07:
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