Lottery numbers The fairness of the South African lot-tery was recently challenged by one of the country’s po-litical parties. The lottery publishes historical statistics at its Website (http://www.nationallottery.co.za/lotto/statistics.aspx). Here is a table of the number of timeseach of the 49 numbers has been drawn in the mainlottery and as the “bonus ball” number as of June 2007: We wonder if all the numbers are equally likely to be the“bonus ball.”a) What kind of test should we perform?b) There are 655 bonus ball observations. What are theappropriate expected value(s) for the test?c) State the null and alternative hypotheses.d) How many degrees of freedom are there?e) The value of x2 is 34.5. What’s the P-value? f) State your conclusion. Number Count Bonus Number Count Bonus1 81 14 26 78 122 91 16 27 83 163 78 14 28 76 74 77 12 29 76 125 67 16 30 99 166 87 12 31 78 107 88 15 32 73 158 90 16 33 81 149 80 9 34 81 1310 77 19 35 77 1511 84 12 36 73 812 68 14 37 64 1713 79 9 38 70 1114 90 12 39 67 1415 82 9 40 75 1316 103 15 41 84 1117 78 14 42 79 818 85 14 43 74 1419 67 18 44 87 1420 90 13 45 82 1921 77 13 46 91 1022 78 17 47 86 1623 90 14 48 88 2124 80 8 49 76 1325 65 11
Lottery numbers The fairness of the South African lot-tery was recently challenged by one of the country’s po-litical parties. The lottery publishes historical statistics at its Website (http://www.nationallottery.co.za/lotto/statistics.aspx). Here is a table of the number of timeseach of the 49 numbers has been drawn in the mainlottery and as the “bonus ball” number as of June 2007: We wonder if all the numbers are equally likely to be the“bonus ball.”a) What kind of test should we perform?b) There are 655 bonus ball observations. What are theappropriate expected value(s) for the test?c) State the null and alternative hypotheses.d) How many degrees of freedom are there?e) The value of x2 is 34.5. What’s the P-value? f) State your conclusion. Number Count Bonus Number Count Bonus1 81 14 26 78 122 91 16 27 83 163 78 14 28 76 74 77 12 29 76 125 67 16 30 99 166 87 12 31 78 107 88 15 32 73 158 90 16 33 81 149 80 9 34 81 1310 77 19 35 77 1511 84 12 36 73 812 68 14 37 64 1713 79 9 38 70 1114 90 12 39 67 1415 82 9 40 75 1316 103 15 41 84 1117 78 14 42 79 818 85 14 43 74 1419 67 18 44 87 1420 90 13 45 82 1921 77 13 46 91 1022 78 17 47 86 1623 90 14 48 88 2124 80 8 49 76 1325 65 11
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 11DE
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Lottery numbers The fairness of the South African lot-
tery was recently challenged by one of the country’s po-
litical parties. The lottery publishes historical statistics at
tery was recently challenged by one of the country’s po-
litical parties. The lottery publishes historical statistics at
its Website (http://www.nationallottery.co.za/lotto/
statistics.aspx). Here is a table of the number of times
each of the 49 numbers has been drawn in the main
lottery and as the “bonus ball” number as of June 2007:
statistics.aspx). Here is a table of the number of times
each of the 49 numbers has been drawn in the main
lottery and as the “bonus ball” number as of June 2007:
We wonder if all the numbers are equally likely to be the
“bonus ball.”
a) What kind of test should we perform?
b) There are 655 bonus ball observations. What are the
appropriate expected value(s) for the test?
c) State the null and alternative hypotheses.
d) How many degrees of freedom are there?
e) The value of x2
“bonus ball.”
a) What kind of test should we perform?
b) There are 655 bonus ball observations. What are the
appropriate expected value(s) for the test?
c) State the null and alternative hypotheses.
d) How many degrees of freedom are there?
e) The value of x2
is 34.5. What’s the P-value?
f) State your conclusion.
Number Count Bonus Number Count Bonus
1 81 14 26 78 12
2 91 16 27 83 16
3 78 14 28 76 7
4 77 12 29 76 12
5 67 16 30 99 16
6 87 12 31 78 10
7 88 15 32 73 15
8 90 16 33 81 14
9 80 9 34 81 13
10 77 19 35 77 15
11 84 12 36 73 8
12 68 14 37 64 17
13 79 9 38 70 11
14 90 12 39 67 14
15 82 9 40 75 13
16 103 15 41 84 11
17 78 14 42 79 8
18 85 14 43 74 14
19 67 18 44 87 14
20 90 13 45 82 19
21 77 13 46 91 10
22 78 17 47 86 16
23 90 14 48 88 21
24 80 8 49 76 13
25 65 11
1 81 14 26 78 12
2 91 16 27 83 16
3 78 14 28 76 7
4 77 12 29 76 12
5 67 16 30 99 16
6 87 12 31 78 10
7 88 15 32 73 15
8 90 16 33 81 14
9 80 9 34 81 13
10 77 19 35 77 15
11 84 12 36 73 8
12 68 14 37 64 17
13 79 9 38 70 11
14 90 12 39 67 14
15 82 9 40 75 13
16 103 15 41 84 11
17 78 14 42 79 8
18 85 14 43 74 14
19 67 18 44 87 14
20 90 13 45 82 19
21 77 13 46 91 10
22 78 17 47 86 16
23 90 14 48 88 21
24 80 8 49 76 13
25 65 11
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