Q 30. Taking the train According to Ne... [FREE SOLUTION]

91影视

The Practice of Statistics for AP

David Moore,Daren Starnes,Dan Yates

$Math Studyset 91影视 Explanations$ Math

4th Edition 路 809 pages

ISBN: 9781319113339

Chapter 5: Q 30. (page 297)

Taking the train According to New Jersey Transit, the 8:00 a.m. weekday train from Princeton to New York City has a 90% chance of arriving on time. To test this claim, an auditor chooses 6 weekdays at random during a month to ride this train. The train arrives late on 2 of those days. Does the auditor have convincing evidence that the company鈥檚 claim isn鈥檛 true? Design and carry out a simulation to answer this question. Follow the four-step process.

Short Answer

Expert verified

The auditor lacks compelling evidence that the company's claim is false.

Step by step solution

Step 1. Given Information

The claim that there is a chance $90 %$ that the train will arrive on schedule. Over the course of a month, a sample of arrival times is taken on $6$ random weekdays. The following is the time of the train's arrival based on the sample taken: $1 - \frac{2}{6} = \frac{4}{6} = 66.6 %$

Step 2. Concept Used

$0$ We can't foresee the outcomes of a chance process, yet they have a regular distribution over a large number of repetitions. According to the law of large numbers, the fraction of times a specific event occurs in numerous repetitions approaches a single number. The likelihood of a chance outcome is its long-run relative frequency. A probability is a number between (never happens) and $1$ (happens frequently) (always occurs).

Step 3. Explanation

We should, in order to simulate, Use two-digit numbers instead of three-digit numbers. The train is on time if the numbers $00$ to $89$ are used. Allow the numbers $90$ to $99$ to symbolise the train's lateness. Pick six numbers at random, with no repeat permitted. Count how many times the train has been late. Rep this simulation as many times as you like. You will most likely get a report indicating that the train is running late between $0$ and $2$ times. As a result, they lack persuasive evidence that the company's claim is false.