Concept explainers
(a)
To State : the hypotheses for testing whether below data give convincing evidence that the distribution of outcomes on Roulette wheel is not as it should be. The following is the scenario.
Roulette Casinos are required to verify that their games operate as advertised. American roulette wheel has 38 slots-18 red, 18 black and 2 green. In one casino, managers record the data from a random sample of 200 spins of one of their American roulette wheels. The one way table is given below.
Color: | Red | Black | Green |
Count: | 85 | 99 | 16 |
(a)
Answer to Problem 2E
H0: There is no significant difference between expected and observed count of red, black and green slots in 200 trails.
Versus
H1: There is significant difference between expected and observed count of red, black and green slots in 200 trails.
Explanation of Solution
The hypotheses here would be
H0: There is no significant difference between expected and observed count of red, black and green slots in 200 trails.
Versus
H1: There is significant difference between expected and observed count of red, black and green slots in 200 trails.
When the roulette wheel is fair meaning that we have equal chance of getting every slot amongst 38 slots, the count of getting a red slot in 200 trails is 18/38×200=94.74 . Similarly count of getting black slot in 200 trails is 18/38×200=94.74 and green slot is 2/38×200=10.52 . These are called expected frequencies or counts.
(b)
To find: expected count for each colour slot.
(b)
Answer to Problem 2E
The expected counts are listed below.
Color: | Red | Black | Green | Total |
Count: | 94.74 | 94.74 | 10.52 | 200 |
Explanation of Solution
When the roulette wheel is fair meaning that we have equal chance of getting every slot amongst 38 slots.
Hence the count of getting a red slot in 200 trails is 18/38×200=94.74 .
Similarly count of getting black slot in 200 trails is 18/38×200=94.74
Green slot is 2/38×200=10.52 .
These are called expected frequencies or counts. These are listed in table below table
Color: | Red | Black | Green | Total |
Count: | 94.74 | 94.74 | 10.52 | 200 |
Chapter 11 Solutions
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