Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 7: Q. 7.44 (page 301)

NBA Champs Repeat parts (b) and (c) of Exercise 7.41 for samples of size 4. For part (b), use your answer to Exercise 7.14(b).

Short Answer

Expert verified

For the samples of size 4, the mean of the variablex¯is μx¯=78.6.

Step by step solution

01

Step 1. Given Information

We have to determine the sample mean for exercise 7.41 for samples of size 4. The given sample in exercise 7.41 as:

02

Step 2. Find the sample mean

In the table below, the samples of size 4 and their respective means are obtained:

SampleHeightMean Height (x¯)
B,W,J,C83,76,80,74
83+76+80+744=78.25
B,W,J,H83,76,80,80
83+76+80+804=79.75
B,W,C,H83,76,74,80
83+76+74+804=78.25
B,J,C,H83,80,74,8083+80+74+804=79.25
W,J,C,H76,80,74,8076+80+74+804=77.5

The variable x¯has the following mean

role="math" localid="1652632975136" μx¯=78.25+79.75+78.25+79.25+77.55μx¯=3935μx¯=78.6

So when the sample size is 4, the variable x¯has a mean μx¯=78.6.

03

Step 3. Find the sample mean using the population mean

We know that mean of the sample mean is equal to the population mean irrespective of the sample size.

Here, for the given data the population mean is μ=78.6.

So the mean of the sample mean of sample size 4 is

μx¯=μ=78.6

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

A variable of a population is normally distributed with mean μand standard deviation σ. For samples of size n, fill in the blanks. Justify your answers.

a. Approximately 68%of all possible samples have means that lie within of the population mean, μ

b. Approximately 95%of all possible samples have means that lie within of the population mean, μ

c. Approximately 99.7%of all possible samples have means that lie within of the population mean, μ

d. 100(1-α)%of all possible samples have means that lie within _of the population mean, μ(Hint: Draw a graph for the distribution of x, and determine the z-scores dividing the area under the normal curve into a middle 1-αarea and two outside areas ofα/2

7.45 NBA Champs. Repeat parts (b) and (c) of Exercise 7.41for samples of size 5. For part (b). use your answer to Exercise 7.15(b).

America's Riches. Each year, Forbes magazine publishes a list of the richest people in the United States. As of September l6, 2013, the six richest Americans and their wealth (to the neatest billion dollars) are as shown in the following table. Consider these six people a population of interest.

(a) For sample size of 6construct a table similar to table 7.2 on page293 what is the relationship between the only possible sample here and the population?

(b) For a random sample of size 6determine the probability that themean wealth of the two people obtained will be within 3(i.e,3 billion) of the population mean. interpret your result in terms of percentages.

7.49 Mobile Homes. According to the U.S. Census Bureau publication Manufactured Housing Statistics, the mean price of new mobile homes is \(65,100. Assume a standard deviation of \)7200. Let x~ denote the mean price of a sample of new mobile homes.
a. For samples of size 50, find the mean and standard deviation of x¯. Interpret your results in words.
b. Repeat part (a) with n=100.

Refer to Exercise 7.7 on page 295.

a. Use your answers from Exercise 7.7(b) to determine the mean, μs, of the variable x¯for each of the possible sample sizes.

b. For each of the possible sample sizes, determine the mean, μs, of the variable x¯, using only your answer from Exercise 7.7(a).
See all solutions

Recommended explanations on Math Textbooks

Applied Mathematics

Read Explanation

Geometry

Read Explanation

Pure Maths

Read Explanation

Calculus

Read Explanation

Logic and Functions

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