Chapter 9, Problem R9.7RE

(a)

To determine

To Explain: the P-value.

Answer to Problem R9.7RE

There is a 0.0384 probability that get 31 successes among 50 trials or more extreme, when the roulette wheel is fair.

Explanation of Solution

Given:

Given claim: Roulette wheel is fair and therefore the ball lends in a read slot 18 times out of 38 on average.

The claim is either the null hypothesis or the alternative hypothesis. The null hypotheses statement is that the population mean is equal to the value given in the claim. If the null hypothesis is the claim then the alternative hypothesis statement is the opposite of null hypothesis.

The P-value is the probability of getting the value of the test statistic or a value more extreme, when the null hypothesis is true.

There is a 0.0384 probability that get 31 successes among 50 trials or more extreme, when the roulette wheel is fair.

(b)

To determine

To Explain: the conclusion would make at the level.

Answer to Problem R9.7RE

There is enough convincing proof that the American roulette wheel is not fair.

Explanation of Solution

Given:

Given claim is that the proportion is 18 out of every 38

Formula used:

Calculation:

The claim is either the null hypothesis or the alternative hypothesis. The null hypotheses statement is that the population mean is equal to the value given in the claim. If the null hypothesis is the claim then the alternative hypothesis statement is the opposite of null hypothesis.

Conditions

The three conditions are: Random, independent, Normal (large counts)

Random: Satisfied, because it is safe to assume that the different spins of the wheel are random.

Independent: satisfied, the reason is that the sample of 50 spins is less than 10% of the population of all spins (assuming that there are more than 500 spins with the roulette wheel).

Normal: Satisfied, because

and are both at least 10.

Since all condition are satisfied, it is suitable to use a hypothesis test for the population proportion

Hypothesis test

The sample proportion is

The test- statistic is

The P-value is the probability of getting the value of the test statistic, or a value more extreme, when the null hypothesis is true. Find the P-value using the normal probability table

If the P-value is lesser than the significance levelthen reject the null hypothesis:

There is enough convincing proof that the American roulette wheel is not fair.

(c)

To determine

To Explain: the responses on the basis of given data.

Answer to Problem R9.7RE

Researcher is correct

Explanation of Solution

Given:

99% confidence level: (0.44, 0.80)

The Researcher is correct.

A 99% confidence interval associates with a significance test at the level.

A 95% confidence interval associates with a significance test at the level.

The significance test at the level and therefore the associating 95% confidence interval, would lead to the opposite conclusion. Thus the there is not enough convincing evidence.