Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q.4 (page 460)

The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean

(a) if the sample size is reasonably large (for any population).

(b) if the population is normally distributed and the sample size is reasonably large.

(c) if the population is normally distributed (for any sample size).

(d) if the population is normally distributed and the population variance is known (for any sample size).

(e) if the population size is reasonably large (whether the population distribution is known or not,

Short Answer

Expert verified

The correct answer is (a) if the sample size is reasonably large (for any population).

Step by step solution

01

Given Information

The central limit theorem is important in statistics because it allows us to use the Normal distribution to make inferences concerning the population mean

02

Explanation

If the population distribution is not Normal, the central limit theorem (CLT) states that when nis large, the sampling distribution of x is approximately Normal.

We know that according to the central limit theorem if the sample size of a sampling distribution is 30or more; then the sampling distribution which has a sample mean x¯is approximately Normal.

Hence, the correct answer is (a).

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

Hispanic workers A factory employs 3000 unionized workers, of whom 30%are Hispanic. The 15 -member union executive committee contains 3 Hispanics. What would be the probability of 3 or fewer Hispanics if the executive committee were chosen at random from all the workers?

CHALLENGE: See if you can compute the probability using another method.

Identify the population, the parameter, the sample, and the statistic in each setting.

Stop smoking! A random sample of 1000people who signed a card saying they intended to quit smoking were contacted nine months later. It turned out that 210(21%)of the sampled individuals had not smoked over the past six months.

The name for the pattern of values that a statistic takes when we sample repeatedly from the same population is

(a) the bias of the statistic.

(b) the variability of the statistic.

(c) the population distribution.

(d) the distribution of sample data.

(e) the sampling distribution of the statistic.

A 10-question multiple-choice exam offers 5choices for each question. Jason just guesses the answers, so he has a probability 1/5of getting any one answer correct. You want to perform a simulation to determine the number of correct answers that Jason gets. One correct way to use a table of random digits to do this is the following:

(a) One digit from the random digit table simulates one answer, with 5=right and all other digits =wrong. Ten digits from the table simulate 10answers. (b) One digit from the random digit table simulates one answer, with 0 or 1 =right and all other digits =wrong. Ten digits from the table simulate 10answers.

(c) One digit from the random digit table simulates one answer, with odd =right and even =wrong. Ten digits from the table simulate 10answers.

(d) Two digits from the random digit table simulate one answer, with 00to 20=right and 21to 99=wrong. Ten pairs of digits from the table simulate 10answers.

(e) Two digits from the random digit table simulate one answer, with 00to 05=right and 06to 99= wrong. Ten pairs of digits from the table simulate 10answers.

Bias and variability The figure below shows his programs of four sampling distributions of different statistics intended to estimate the same parameter.

(a) Which statistics are unbiased estimators? Justify your answer. (b) Which statistic does the best job of estimating the parameter? Explain.
See all solutions

Recommended explanations on Math Textbooks

Statistics

Read Explanation

Theoretical and Mathematical Physics

Read Explanation

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Discrete Mathematics

Read Explanation

Logic and Functions

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