Consider the following sequence of (0,1) random numbers: 0.943 0.398 0.372 0.943
ID: 3297202 • Letter: C
Question
Consider the following sequence of (0,1) random numbers:
0.943
0.398
0.372
0.943
0.204
0.794
0.498
0.528
0.272
0.899
0.294
0.156
0.102
0.057
0.409
0.398
0.401
0.997
Test if the sequence is distributed U (0, 1) using a Chi-Squared test with 5 equally spaced intervals.
LL
UL
Observed
Expected
(O-E)^2/E
1
0.0
0.2
3
0.1
2
0.2
0.4
3
0.4
0.6
4
0.044444
4
0.6
0.8
1
1.877777
5
0.8
1.0
4
0.044444
18
Test Statistic =
# intervals
5
df
The expected number in each interval is?
0.943
0.398
0.372
0.943
0.204
0.794
0.498
0.528
0.272
0.899
0.294
0.156
0.102
0.057
0.409
0.398
0.401
0.997
Explanation / Answer
expected = total /number of interval = 18/5 = 3.6
df = number of interval -1 = 5-1 = 4
critical value = 9.48
since TS = 3.666 < critical value, we fail to reject the null
Please rate my solution
LL UL Observed Expected (O-E)^2/E 1 0 0.2 3 3.6 0.1 2 0.2 0.4 6 3.6 1.6 3 0.4 0.6 4 3.6 0.044444 4 0.6 0.8 1 3.6 1.877777 5 0.8 1 4 3.6 0.044444 18 Test Statistic = 3.666665 df 4