Powerball is a large lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the "Powerball." If you select the correct number on the Powerball, your winnings will be increased. The possible numbers for the Powerball are 1 through 35. If the selection is random, then there should be an equal number of draws for the Powerball across the following 5 categories: 1-7, 8-14, 15-21, 22-28, 29-35. Test at 1% significance that Powerball numbers are equally likely. Round to the fourth as needed.
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
Powerball is a large lottery in which players try to guess the numbers that will turn up in a drawing of numbered balls. One of the balls drawn is the "Powerball." If you select the correct number on the Powerball, your winnings will be increased. The possible numbers for the Powerball are 1 through 35. If the selection is random, then there should be an equal number of draws for the Powerball across the following 5 categories: 1-7, 8-14, 15-21, 22-28, 29-35. Test at 1% significance that Powerball numbers are equally likely.
Round to the fourth as needed.
| Powerball Number | Observed Frequency |
Expected Frequency |
|---|---|---|
| 1-7 | 43 | |
| 8-14 | 40 | |
| 15-21 | 45 | |
| 22-28 | 45 | |
| 29-35 | 42 |
Test Statistic:
Degrees of Freedom:
p-val:
Decision Rule: Select an answer Accept the Null Reject the Null Fail to Reject the Null
Did something significant happen? Select an answer:
Significance Happened
Nothing Significant Happened
There Select an answer is or is not enough evidence to conclude
Select an answer that the results for the Powerball are not equally likely or that the results for the Powerball are equally likely
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