Logout Open In App
Open In App
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

Chapter 5: Q15E (page 314)

Will the sampling distribution of x¯always be approximately normally distributed? Explain

Short Answer

Expert verified

Answer

A sampling distribution is statistics derived by continuous sampling from a greater populace.

Step by step solution

01

Step-by-Step Solution Step 1: Sampling distribution

A sampling distributionis a probabilistic distribution of a statistic resulting from the selection of randomized samples from a particular population. It reflects the distribution of frequency on how far apart certain events will be for a specific demographic.

02

Explanation

No, since the central limit theorem asserts that if the sample size increases sufficient, the sampling distributions of x overbar are nearly distributed normally.

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

Consider the following probability distribution:

a. Calculate for this distribution.

b. Find the sampling distribution of the sample mean for a random sample of n = 3 measurements from this distribution, and show that is an unbiased estimator of .

c. Find the sampling distribution of the sample median for a random sample of n = 3 measurements from this distribution, and show that the median is a biased estimator of .

d. If you wanted to use a sample of three measurements from this population to estimate , which estimator would you use? Why?

:A random sample of n = 68 observations is selected from a population withμ=19.6and σ=3.2Approximate each of the following probabilities

a)pX¯⩽19.6

b)pX¯⩽19

c)pX¯⩾20.1

d)p19.2⩽X¯⩽20.6

Consider the population described by the probability distribution shown below.

The random variable x is observed twice. If these observations are independent, verify that the different samples of size 2 and their probabilities are as shown below.

a. Find the sampling distribution of the sample meanx.

b. Construct a probability histogram for the sampling distribution ofx.

c. What is the probability thatxis 4.5 or larger?

d. Would you expect to observe a value ofxequal to 4.5 or larger? Explain.

A random sample of n = 64 observations is drawn from a population with a mean equal to 20 and a standard deviation equal to 16

a. Give the mean and standard deviation of the (repeated) sampling distribution of x.

b. Describe the shape of the sampling distribution of x. Does your answer depend on the sample size?

c. Calculate the standard normal z-score corresponding to a value of x = 15.5.

d. Calculate the standard normal z-score corresponding to x = 23

A random sample of n = 80 measurements is drawn from a binomial population with a probability of success .3.

  1. Give the mean and standard deviation of the sampling distribution of the sample proportion, p¯
  2. Describe the shape of the sampling distribution of p¯
  3. Calculate the standard normal z-score corresponding to a value of p¯=0.35
  4. FindP(p)¯=0.35
See all solutions

Recommended explanations on Math Textbooks

Geometry

Read Explanation

Applied Mathematics

Read Explanation

Calculus

Read Explanation

Pure Maths

Read Explanation

Mechanics Maths

Read Explanation

Probability and Statistics

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