Log In Start studying!

Select your language

Suggested languages for you:

Americas

English (US)

Europe

7.40

Expert-verified

Elementary Statistics

Found in: Page 300

Book edition 9th

Author(s) Weiss, Neil

Pages 590 pages

ISBN 9780321989505

Answers without the blur.

Just sign up for free and you're in.

Register for Free I’ll do it later

Short Answer

Refer to Exercise $7.10$ on page $295$ .
a. Use your answers from Exercise $7.10 (b)$ to determine the mean, $μ_{i}$ , of the variable $\hat{x}$ for each of the possible sample sizes.
b. For each of the possible sample sizes, determine the mean, $μ_{i +}$ of the variable $\hat{x}$ , using only your answer from Exercise $7.10 (a)$

The mean $μ_{\bar{x}}$ of the variable $\bar{x}$ will be $5$ .
The population mean of the given data is $5$

See the step by step solution

Step by Step Solution

TABLE OF CONTENTS :

TABLE OF CONTENTS

Part (a) Step 1: Given information

Given in the question that

Population data: $2, 3, 5, 5, 7, 8$ .

Part (a) Step 2: Calculation of the mean

The population data for the variable $x$ is $2, 3, 5, 5, 7, 8$

Here determine the role="math" localid="1651232434578" $μ_{\bar{x}}$ of the variable $\bar{x}$ for each sample in the question

The possible sample and sample means for a sample of size $n = 1$ is given in the table

$\begin{array}{l} Sample & \bar{x} \\ 2 & 2 \\ 3 & 3 \\ 5 & 5 \\ 5 & 5 \\ 7 & 7 \\ 8 & 8 \end{array}$

Therefore the mean $μ_{\bar{x}}$ of the variable $\bar{x}$ will be,

role="math" localid="1651232793762" $μ_{\bar{x}} = \frac{2 + 3 + 5 + 5 + 7 + 8}{6} = \frac{30}{6} = 5^{6}$

The mean $μ_{\bar{x}}$ of the variable $\bar{x}$ will be $5$

Part (a) Step 3: Calculation

Now we need to calculate the possible sample and sample means for sample of size $n = 2$

The table will be

$\begin{array}{l} Sampie & \bar{x} & Sample & \bar{x} \\ 2.3 & 2.5 & 3.7 & 5 \\ 2.5 & 3.5 & 3.8 & 5.5 \\ 2.5 & 3.5 & 5.5 & 5 \\ 2, 7 & 4.5 & 5, 7 & 6 \\ 2, 8 & 5 & 5, 8 & 6.6 \\ 3, 5 & 4 & 5, 7 & 6 \\ 3.5 & 4 & 5.8 & 6.5 \\ 7.8 & 7.5 \end{array}$

The mean $μ_{\bar{x}}$ for the variable $\bar{x}$ will be

role="math" localid="1651234078644" $μ_{x} = \frac{\{\begin{array}{l} 3.3 + 3.3 + 4 + 4.3 + 4 + 4.7 + 5 + 4.7 + 5 + 5.7 + 4.3 + 5 + 5.3 + 5 + \\ 5.3 + 6 + 5.7 + 6 + 6.7 + 6.7 \end{array}\}}{20} = \frac{100}{20} = 5$

The mean $μ_{\bar{x}}$ of the variable $\bar{x}$ when sample size $n = 2$ is $5$

Part (b) Step 1: Given information

Given in the question that

Population data: $2, 3, 5, 5, 7, 8$ .

Part (b) Step 2: Explanation

Here we need to find the population mean

The calculation for the population mean will be,

$μ = \frac{\sum x_{i}}{N} = \frac{2 + 3 + 5 + 5 + 7 + 8}{6} = 5$

So, The population mean will be $5$ .

Most popular questions for Math Textbooks

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

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 $4$ construct a table similar to table 7.2 on page293.(There are 15 possible sample of size $4$

(b) For a random sample of size $4$ determine 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.

A variable of a population has mean μ and standard deviation $σ$ . that For a large sample size n, answer the following questions.

a. Identify the distribution of $x .$

b. Does your answer to part (a) depend on n being large? Explain your answer.

c. Identify the mean and the standard deviation of $x .$

d. Does your answer to part (c) depend on the sample size being large? Why or why not?

7.51 Earthquakes. According to The Earth: Structure, Composition and Evolution (The Open University, S237), for earthquakes with a magnitude of $7.5$ or greater on the Richter scale, the time between successive earthquakes has a mean of $437$ days and a standard deviation of $399$ days. Suppose that you observe a sample of four times between successive earthquakes that have a magnitude of $7.5$ or greater on the Richter scale.
a. On average, what would you expect to be the mean of the four times?b. How much variation would you expect from your answer in part (a)? (Hint: Use the three-standard-deviations rule.)

Ethanol Railroad Tariffs. An ethanol railroad tariff is a fee charged for shipments of ethanol on public railroads. The Agricultural Marketing Service publishes tariff rates for railroad-car shipments of ethanol in the Biofuel Transportation Database. Assuming that the standard deviation of such tariff rates is $$ 1, 150$ , determine the probability that the mean tariff rate of $500$ randomly selected railroad car shipments of ethanol will be within $$ 100$ of the mean tariff rate of all railroad-car shipments of ethanol. Interpret your answer in terms of sampling error.

Want to see more solutions like these?

Sign up for free to discover our expert answers

Get Started - It’s free

Recommended explanations on Math Textbooks

94% of StudySmarter users get better grades.

Sign up for free