The mean of the population _______________, is equal to, greater to, or less to the mean of the sample means, _______________. C.) Does the sample means target the value of the population mean? In general, do sample means make good estimates of population mean ? Why or why not? The sample means do not target or target the population mean. In general, sample means do or do not make good estimates of population means because the mean is an unbiased or biased estimator. The data provided concerns the assets (in billions of dollars) of the four wealthiest people in a particular country, listed as 45, 28, 21, and 18. The exercise is to assume that samples of size n = 2 are randomly selected with replacement from this population of four values.### Task:a. After identifying the 16 possible samples and calculating the mean of each sample, construct a table to show the sampling distribution of the sample mean. In this table, values of the sample mean that are the same are combined.### Table Layout:#### \( \bar{x} \) - Probability- **45:** [Probability]- **36.5:** [Probability]- **33:** [Probability]- **31.5:** [Probability]- **28:** [Probability]- **24.5:** [Probability]- **23:** [Probability]- **21:** [Probability]- **19.5:** [Probability]- **18:** [Probability](Type integers or fractions.)The table reflects the calculation of probabilities after determining the means of all possible sampled pairs. Each mean is accompanied by a placeholder for its respective probability, which should be filled as integer or fractional values. **Instructional Text for Educational Website:**---**b. Comparing Population Mean and Sample Mean:**In this section, you are asked to analyze the relationship between the mean of the population and the mean of the sampling distribution of the sample mean. - The mean of the population, represented as \(\_\_\), is [dropdown box: greater than, less than, equal to] the mean of the sample means, represented as \(\_\_\).*Note: Please round your answer to two decimal places as needed.*---**c. Evaluating Sample Means as Estimators of Population Means:**This part encourages you to consider whether sample means can accurately target or represent the population mean.- The sample means [dropdown box: target, do not target] the population mean. Generally, sample means [dropdown box: do, do not] make good estimates of population means because the mean is a [dropdown box: unbiased, biased] estimator.---No graphs or diagrams are included in this section.

The question is about sampling distribution Given : Popl. data : 45, 28, 21, 18 Randomly selected…

Answered: The assets (in billions of dollars) of…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

See similar textbooks

Related questions

Question

100%

The mean of the population _______________, is equal to, greater to, or less to the mean of the sample means, _______________.

C.) Does the sample means target the value of the population mean? In general, do sample means make good estimates of population mean ? Why or why not?

The sample means do not target or target the population mean. In general, sample means do or do not make good estimates of population means because the mean is an unbiased or biased estimator.

The data provided concerns the assets (in billions of dollars) of the four wealthiest people in a particular country, listed as 45, 28, 21, and 18. The exercise is to assume that samples of size n = 2 are randomly selected with replacement from this population of four values.

### Task:
a. After identifying the 16 possible samples and calculating the mean of each sample, construct a table to show the sampling distribution of the sample mean. In this table, values of the sample mean that are the same are combined.

### Table Layout:

#### \( \bar{x} \) - Probability
- **45:** [Probability]
- **36.5:** [Probability]
- **33:** [Probability]
- **31.5:** [Probability]
- **28:** [Probability]
- **24.5:** [Probability]
- **23:** [Probability]
- **21:** [Probability]
- **19.5:** [Probability]
- **18:** [Probability]

(Type integers or fractions.)

The table reflects the calculation of probabilities after determining the means of all possible sampled pairs. Each mean is accompanied by a placeholder for its respective probability, which should be filled as integer or fractional values.

**Instructional Text for Educational Website:**

---

**b. Comparing Population Mean and Sample Mean:**

In this section, you are asked to analyze the relationship between the mean of the population and the mean of the sampling distribution of the sample mean.

- The mean of the population, represented as \(\_\_\), is [dropdown box: greater than, less than, equal to] the mean of the sample means, represented as \(\_\_\).

*Note: Please round your answer to two decimal places as needed.*

---

**c. Evaluating Sample Means as Estimators of Population Means:**

This part encourages you to consider whether sample means can accurately target or represent the population mean.

- The sample means [dropdown box: target, do not target] the population mean. Generally, sample means [dropdown box: do, do not] make good estimates of population means because the mean is a [dropdown box: unbiased, biased] estimator.

---

No graphs or diagrams are included in this section.

Definition Definition Measure of central tendency that is the average of a given data set. The mean value is evaluated as the quotient of the sum of all observations by the sample size. The mean, in contrast to a median, is affected by extreme values. Very large or very small values can distract the mean from the center of the data. Arithmetic mean: The most common type of mean is the arithmetic mean. It is evaluated using the formula: μ = 1 N ∑ i = 1 N x i Other types of means are the geometric mean, logarithmic mean, and harmonic mean. Geometric mean: The nth root of the product of n observations from a data set is defined as the geometric mean of the set: G = x 1 x 2 ... x n n Logarithmic mean: The difference of the natural logarithms of the two numbers, divided by the difference between the numbers is the logarithmic mean of the two numbers. The logarithmic mean is used particularly in heat transfer and mass transfer. ln x 2 − ln x 1 x 2 − x 1 Harmonic mean: The inverse of the arithmetic mean of the inverses of all the numbers in a data set is the harmonic mean of the data. 1 1 x 1 + 1 x 2 + ...

Expert Solution