**Educational Content: Understanding Sampling Distributions**---According to a recent survey, the population distribution of the number of years of education for self-employed individuals in a certain region has a mean of \( 14.5 \) and a standard deviation of \( 2.8 \).### Problem Analysis1. **Identify the Random Variable:** - **Correct Description:** The number of years of education is the random variable of interest.2. **Sampling Distribution of Sample Mean:** - **Mean of the Sampling Distribution (Sample Size: 49):** - The mean is \( 14.5 \). - **Correct Description of Mean:** - The expected value for the mean of a sample of size 49.3. **Determine the Standard Deviation:** - Calculate the standard deviation for the sample mean using the formula for the standard deviation of the sampling distribution: \[ \text{Standard Deviation}_{\bar{x}} = \frac{\sigma}{\sqrt{n}} \] where \(\sigma\) is the population standard deviation, and \(n\) is the sample size.### Interpretation- **Repeat for \( n = 196 \):** Analyze and compare the effects as the sample size increases. Generally, as the sample size \( n \) increases, the standard deviation of the sampling distribution decreases, making the sample means closer to the population mean.---This content provides an overview of how to interpret measures and variations within sampling distributions, crucial for statistical analysis and educational insights.

Answered: Image /qna-images/answer/976c7473-f3b8-4eca-b61b-5008bb512552.jpg

Answered: According to a recent survey, the…

MATLAB: An Introduction with Applications

6th Edition

ISBN:9781119256830

Author:Amos Gilat

Publisher:Amos Gilat

Chapter1: Starting With Matlab

Section: Chapter Questions

Problem 1P

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The distribution of the number of motor vehicles per household in the United States (the population) and sampling distributions of the mean for samples of size 4 and 10 are shown in below. A.Which distribution is which? Make a rough estimate of the mean and standard deviation of each distribution. Explain the reasons of your choices.b. The mean of the population is about 1.7. Theoretically, what is the mean of the sampling distribution for samples of size 4? Of size 10? Are these computed means consistent with your estimates of the means in the histograms? Briefly explain.c. The standard deviation of the population is about 1. Theoretically, what is the Standard Error (SE) of the sampling distribution for samples of size 4? Of size 10? Are these computed SEs consistent with your estimates of the SEs in the histograms? Briefly explain.d. Compare the shapes of the three distributions. Are the shapes consistent with the Central Limit Theorem? Briefly explain.
1. Compute the variance of the number of boats sold daily (show your calculation prices in a table) 2. Compute the standard deviation of the number of boats sills daily.
For a population that has a standard deviation of 22, figure the standard deviation of the distribution of means for samples of size (a)2, (b)4, (c)5 and (d)10.
What is the mean and standard deviation of the sampling distribution of X¯X¯ for n = 16, if the sampled population has a mean of 48 and a standard deviation of 12? Select one: a. 4 and 1 b. 12 and 3 c. 48 and 3 d. 48 and 1 e. 48 and 12
The degrees of freedom used when testing two independent samples where the population standard deviation is unknown is Group of answer choices a.n1 + n2 - 2. b.the smaller of n1 - 1 or n2 - 1. c.n1 + n2 - 1. d.the larger of n1 - 1 or n2 - 1.
Suppose a simple random sample of size n= 50 is obtained from a population whose size is N= 10,000 and whose population proportion with a specified characteristic is p= 0.4. Click here to view the standard normal distribution table (page 1). Click here to view the standard normal distribution table (page 2). (a) Describe the sampling distribution of p. Choose the phrase that best describes the shape of the sampling distribution below. YA. Approximately normal because ns0.05N and np(1- p) 2 10. O B. Approximately normal because ns0.05N and np(1- p) < 10. O C. Not normal because ns 0.05N and np(1 - p) 2 10. O D. Not normal because ns0.05N and np(1- p) < 10. Determine the mean of the sampling distribution of p. HA = (Round to one decimal place as needed.)
B. Samples of size n were randomly selected from the population. The mean and the standard deviations of the population are given below. In each case, find the mean and the variance of the sampling distribution of the means. μ = 3; o = 1.3 1. n = 2; 2. n = 5; μ = 2.75; o = 3.5 3. n = 8; μ = 32; o = 7.9 n = 6; μ = 4.3; o = 1.9 4. 5. n = 2; μ = 1.5; o = 2
Which of the following are true? There is more than one correct answer.
A random sample of n = 78 measurements is drawn from a binomial population with probability of success 0.2. Complete parts a through d below. a. Give the mean and standard deviation of the sampling distribution of the sample proportion, p. The mean of the sampling distribution of p is The standard deviation of the sampling distribution of p is (Round to four decimal places as needed.) b. Describe the shape of the sampling distribution of p. OA. The shape of the sampling distribution of p is approximately normal because the sample size is large. OB. The shape of the sampling distribution of p is approximately uniform because the sample size is large. OC. The shape of the sampling distribution of p is approximately normal because the sample size is small. OD. The shape of the sampling distribution of p is approximately uniform because the sample size is small. c. Calculate the standard normal'z-score corresponding to a value of p = 0.32. The standard normal z-score corresponding to a…
Solve part a,b and c of practice question #2. Please and thank you.
answer d)

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