Chapter 11.1, Problem 2E

(a)

To determine

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

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 determine

To find: expected count for each colour slot.

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