Login Registrieren

Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

The Practice of Statistics for AP Examination

Daren Starnes, Josh Tabor

$Math Studyset Vaia Explanations$ Math

6th Edition · 837 pages

ISBN: 9781319113339

Chapter 7: Q. 70 (page 481)

What does the CLT say? Asked what the central limit theorem says, a student replies, "As you take larger and larger samples from a population, the variability of the sampling distribution of the sample mean decreases." Is the student right? Explain your answer.

Short Answer

Expert verified

The statement made by the student is Yes, correct

Step by step solution

01

Given information

The student made a statement "The variability of the sampling distribution of the sample mean diminishes as you take more and larger samples from a population."

02

Explanation

If the sample size is higher than or equal to 30, the sampling distribution of the sample mean will be nearly normal with mean and standard deviation, according to the central limit theorem is $σ / \sqrt{n}$ .

The standard deviation of the sampling distribution drops as the value of n increases, and the spread of the sampling distribution of the sample mean decreases.

Unlock Step-by-Step Solutions & Ace Your Exams!

Full Textbook Solutions
Get detailed explanations and key concepts
Unlimited Al creation
Al flashcards, explanations, exams and more...
Ads-free access
To over 500 millions flashcards
Money-back guarantee
We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

Lightning strikes The number of lightning strikes on a square kilometer of open ground in a year has mean 6 and standard deviation 2.4. The National Lightning Detection Network (NLDN) uses automatic sensors to watch for lightning in 1-square-kilometer plots of land. Find the probability that the total number of lightning strikes in a random sample of 50 square-kilometer plots of land is less than $250$ .

$10 %$ Why is it important to check the 10 % condition before calculating probabilities involving localid="1654670795605">x-?

a. To reduce the variability of the sampling distribution of $x^{-} \bar{x}$

b. To ensure that the distribution of $x^{-} \bar{x}$ is approximately Normal

c. To ensure that we can generalize the results to a larger population

d. To ensure that $x^{-} \bar{x}$ will be an unbiased estimator of $μ$

e. To ensure that the observations in the sample are close to independent

David’s iPod has about $10, 000$ songs. The distribution of the play times for these songs is heavily skewed to the right with a mean of $225$ seconds and a standard deviation of $60$ seconds.

a. Describe the shape of the sampling distribution of $x$ for SRSs of size $n = 5$ from the population of songs on David’s iPod. Justify your answer.

b. Describe the shape of the sampling distribution of $x$ for SRSs of size $n = 100$ from the population of songs on David’s iPod. Justify your answer.

Bag check Thousands of travelers pass through the airport in Guadalajara, Mexico, each day. Before leaving the airport, each passenger must pass through the customs inspection area. Customs agents want to be sure that passengers do not bring illegal items into the country. But they do not have time to search every traveler's luggage. Instead, they require each person to press a button. Either a red or a green bulb lights up. If the red light flashes, the passenger will be searched by customs agents. A green light means "Go ahead." Customs agents claim that $30 %$ of all travelers will be stopped (red light), because the light has probability of showing red on any push of the button. To test this claim, a concerned citizen watches a random sample of 100 travelers push the button. Only 20 get a red light.

a. Assume that the customs agents' claim is true. Find the probability that the proportion of travelers who get a red light in a random sample of 100 travelers is less than or equal to the result in this sample.

b. Based on your results in part (a), is there convincing evidence that less than $30 %$ of all travelers will be stopped? Explain your reasoning.

Making auto parts Refer to Exercise 54 . How many axles would you need to sample if you wanted the standard deviation of the sampling distribution of $x - \bar{x}$ to be $0.0005 mm$ ? Justify your answer.

See all solutions

Recommended explanations on Math Textbooks

Discrete Mathematics

Read Explanation

Probability and Statistics

Read Explanation

Decision Maths

Read Explanation

Geometry

Read Explanation

Statistics

Read Explanation

Calculus

Read Explanation

View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free