**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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A simple random sample of 10 UE students were taken to estimate the mean (μ) weekly allowance of all UE students. The data are: 500 550 600 1000 675 450 500 650 800 825 1. Construct a 95% C.I. on μ and interpret. 2. Construct a 99% C.I. on μ and interpret.
Exhibit 11-3 The contents of a sample of 26 cans of apple juice showed a standard deviation of 0.06 ounce. We are interested in testing to determine whether the variance of the population is significantly more than .003. Refer to Exhibit 11-3. The p-value for this test is a) .05 b) greater than .10 c) less than .10 d) 1.96
A boat capsized and sank in a lake. Based on an assumption of a mean weight of 133 Ib, the boat was rated to carry 70 passengers (so the load limit was 9,310 Ib). After the boat sank, the assumed mean weight for similar boats was changed from 133 lb to 174 lb. Complete parts a and b below. a. Assume that a similar boat is loaded with 70 passengers, and assume that the weights of people are normally distributed with mean of 181.1 Ib and a standard deviation of 38.6 lb. Find the probability that the boat is overloaded because the 70 passengers have mean weight greater than 133 lb The probability isO: (Round to four decimal places as needed.) b. The boat was later rated to carry only 17 passengers, and the load limit was changed to 2,958 Ib. Find the probability that the boat is overloaded because the mean weight of the passengers is greater than 174 (so that their total weight is greater than the maximum capacity of 2,958 Ib). The probability is. (Round to four decimal places as needed.)…
Consider the data from the Anthropology 105 class. The mean for women is 64.33 in and the standard deviation is 2.64 in. The average height of men in the US is approximately 5ft 10in. What proportion of women represented here are shorter than the average man?
A population has a mean µ = 87 and a standard deviation à = 23. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 257. ox = (Simplify your answer.) (Type an integer or decimal rounded to three decimal places as needed.) 33
A population has a mean µ = 70 and a standard deviation o = 28. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 261. P = (Simplify your answer.) = (Type an integer or decimal rounded to three decimal places as needed.)
A researcher would like to evaluate the effectiveness of a pain-relief patch designed for back pain. Prior to testing the patch, each of n = 8 patients rates their current level of back pain on a scale from 1 to 10. After wearing the patch for 90 minutes, a second pain rating is recorded. The data are as follows: Before After 6 2 8 3 9 4 8 1 10 2 5 3 9 8 7 7 a. Compute the mean and variance for the sample of difference scores. b. Do the results indicate that the pain-relief patch has an effect? Use a two-tailed test with α = .05 c. Compute Cohen’s d to measure the size of the effect.
A population has a mean u= 81 and a standard deviation o = 21. Find the mean and standard deviation of a sampling distribution of sample means with sample size n = 255. (Simplify your answer.) (Type an integer or decimal rounded to three decimal places as needed.)
The owner of a fish market has an assistant who has determined that the weights of catfish are normally distributed, with a mean of 3.2 pounds and a standard deviation of 0.8 pound. If a sample of 25 fish yields a mean of 3.1 pounds, what is the Z-score for this observation? Question 3 options: 1) 2.500 2) 0.625 3) -0.625 4) 1.250

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