The author recorded all digits selected in New Yorks Win 4 Lottery for two drawi
ID: 3239078 • Letter: T
Question
The author recorded all digits selected in New Yorks Win 4 Lottery for two drawings held each day in a recent year. The frequencies of the digits from 0 through 9 are 280, 303, 331, 289, 285, 294, 283, 274, 297, and 284. Use a 0.05 significance level to test the claim of lottery officials that the digits are selected in a way that they are equally likely. Police Calls The police department in Madison, Connecticut released the following numbers of calls for the different days of the week during a recent February that had 28 days:Monday (114):Tuesday (152):Wednesday (160):Thursday (164):Friday (179):Saturday (196):Sunday (130). Use a 0.01 significance level to test the claim that the different days of the week have the same frequencies of police calls. Is there anything notable about the observed frequencies? Repeat the preceding exercise using these observed frequencies for police calls received during the month of March:Monday (208):Tuesday (224):Wednesday (246):Thursday (173):Friday (210):Saturday (236):Sunday (154). What is a fundamental error with this analysis?Explanation / Answer
Answer:
Multiple questions; 2 questions answered.
14).
Ho: Digits are selected equally likely.
H1: Digits are selected not equally likely.
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
280
292.000
-12.000
0.493
303
292.000
11.000
0.414
331
292.000
39.000
5.209
289
292.000
-3.000
0.031
285
292.000
-7.000
0.168
294
292.000
2.000
0.014
283
292.000
-9.000
0.277
274
292.000
-18.000
1.110
297
292.000
5.000
0.086
284
292.000
-8.000
0.219
Total
2920
2920.000
8.021
8.021
chi-square
9
df
.5321
p-value
Calculated chi square 8.021 < critical value 16.92. Ho is not rejected.
We conclude that Digits are selected equally likely.
15).
Ho:Different days of the week have same frequencies
H1: Different days of the week have different frequencies
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
114
156.429
-42.429
11.508
152
156.429
-4.429
0.125
160
156.429
3.571
0.082
164
156.429
7.571
0.366
179
156.429
22.571
3.257
196
156.429
39.571
10.010
130
156.429
-26.429
4.465
Total
1095
1095.000
29.814
29.81
chi-square
6
df
0.0000
p-value
Calculated chi square 29.81 > critical value 16.81. Ho is rejected.
We conclude that different days of the week have different frequencies.
Goodness of Fit Test
observed
expected
O - E
(O - E)² / E
280
292.000
-12.000
0.493
303
292.000
11.000
0.414
331
292.000
39.000
5.209
289
292.000
-3.000
0.031
285
292.000
-7.000
0.168
294
292.000
2.000
0.014
283
292.000
-9.000
0.277
274
292.000
-18.000
1.110
297
292.000
5.000
0.086
284
292.000
-8.000
0.219
Total
2920
2920.000
8.021
8.021
chi-square
9
df
.5321
p-value
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