6. What **NOT** true about the CLT (Central limit theorem)? * As long as sample sizes are greater than 30, the mean of the sample means (mu of X- bars) is = population mean (mu) As long as the parent population is normal, the sample means will be normally distributed, regardless of sample size 句。 the sampling distribution of the sample means (X-bars) is normally distributed, regardless of sample size The standard deviation of the of the X-bars = sigma / SQRT(N) 火 Send To →)

6. What NOT true about the CLT (Central limit theorem)? * As long as sample sizes are greater than 30, the mean of the sample means (mu of X- bars) is = population mean (mu) As long as the parent population is normal, the sample means will be normally distributed, regardless of sample size 句。 the sampling distribution of the sample means (X-bars) is normally distributed, regardless of sample size The standard deviation of the of the X-bars = sigma / SQRT(N) 火 Send To →)

Name: Question 6 6. What **NOT** true about the CLT (Central limit theorem)?
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Description: Question 6 6. What **NOT** true about the CLT (Central limit theorem)? *As long as sample sizes are greater than 30, the mean of the sample means (mu of X-bars) is = population mean (mu)As long as the parent population is normal, the sample means wil

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 Central Limit Theorem is one of the most important and useful concepts of statistics. It forms a foundation for estimating population parameters and hypothesis testing and states that as the sample size increases, the sampling distribution of sample means approaches an FF distribution, regardless of the distribution of the original population. as the sample size increases, the sampling distribution of sample means approaches a Binomial distribution, regardless of the distribution of the original population. as the sample size increases, the sampling distribution of sample means approaches a Student (tt) distribution, regardless of the distribution of the original population. as the sample size increases, the sampling distribution of sample means approaches a Chi-square (χ2χ2) distribution, regardless of the distribution of the original population. as the sample size increases, the sampling distribution of sample means approaches a Normal (zz) distribution, regardless of the…
Recall also that for large sample values, the Central Limit Theorem applies. That is, as the sample size n increases without limit, the shape of the distribution of the sample means taken from the population with mean μμ, and standard deviation σσ, will approach a normal distribution. So, with the application of the Central Limit Theorem, approximately 95% of the sample means taken from a population will fall within ±1.96±1.96standard errors of the population mean. Thus, the interval estimate is given by, μ−1.96(σn√)toμ+1.96(σN√)μ−1.96(σn)toμ+1.96(σN) The General Formula for confidence intervals for large samples is: lower confidence boundary or limit < population mean< upper confidence boundary or limit X−zα2(σn√)<μ<X+zα2(σn√)X−zα2(σn)<μ<X+zα2(σn) Also consider the following: Confidence Level zα2valueszα2values (confidence coefficients) 90% ±1.645±1.645 95% ±1.96±1.96 99% ±2.58±2.58 A Four-step Process in Computing the Interval Estimates Step…
2) A manufacturer claims that the replacement time for their CD players has a mean of 7 years and a standard deviation of 1.4 years. If this is true, find the probability that a) one randomly selected CD player is replaced in 6.2 years or less b) in a random sample of 30 CD players, the mean replacement time is 6.2 years or less c) In part b), are the assumptions of the Central Limit Theorem satisfied? Explain
This is about central limit theorem, can someone help me? 1. The average number of liters of fresh milk that a person consumes in a month is 18 liters. Assume that the standard deviation is 4.5 liters and the distribution is approximately normal. a. Find the probability that a person selected at random consumes more than 16 liters per month. b. If a sample of 32 individuals is selected , find the probability that mean of the sample will be more than 16 liters.
3. The length of time taken on the SAT for a group of students is normally distributed with a mean of 2.5 hours and a standard deviation of 0.25 hours. A sample size of n = 60 is drawn randomly from the population. Find the probability that the sample mean is between two hours and three hours. Calculate the standard deviation from the CLT ( Central Limit Theorem) to 4 places.
A simple random sample of size n=10 is obtained from a population that is normally distributed with a mean of 40 and a standard deviation of 3. Is the sampling distribution normally distributed? Why? Yes, the sampling distribution is normally distributed because the population is normally distributed. Yes, the sampling distribution is normally distributed because the population mean is greater than 30. No, the sampling distribution is not normally distributed because the population is not normally distributed. No, the sampling distribution is not normally distributed because the sample size is less than 30.
According to the stock index, the return from January 2014 to December 2014 shows the average of 7% with standard deviation of 2.5%. 1) According to the Central Limit Theorem (CLT), what the sample mean distribution if we randomly pick 25 stocks? 2) What is the probability that the sample mean is higher than 8% if we randomly select 25 stocks? 3) What is the probability that the sample mean is lower than 6.5% if we randomly select 100 stocks? 4) Suppose the population mean is unknown, but we know the population standard deviation is 2.5. What is the 95% confidence interval of population mean if the sample mean is 7.2$ and the sample standard deviation is 3% from randomly selected 25 stocks?
Mario made a claim that 95% of college male students in their school join triathlon. His friend, Baste, finds this hard to believe and decided to check the validity of such claim, so he took a random sample and found out that 75 out of 90 had joined the race. 1. What is the population proportion? 2. What is the sample proportion? 3. Is the sample large enough to use the Central Limit Theorem?
3) The Medical College Admission Test (MCAT) has scores that are normally distributed with a mean of 25 and a standard deviation of 6.5. In a random sample of 25 students, what is the probability that their mean score is between 22 and 28? Are the assumptions of the Central Limit Theorem satisfied?
Consider the following. In case that the Central Limit Theorem is NOT applicable, enter 0 as your answer. Otherwise, your answer must be in FOUR DECIMAL places. In a town, the mean weight of male adults is 73kg with a standard deviation of 12kg. Suppose that 50 male adults are randomly chosen for a study. What is the probability that their mean weight is less than 75kg? Suppose that 12 male adults are randomly chosen. What is the probability that their mean weight is between 80kg and 85kg? Assume that the distribution of weights of male adults are normally distributed.
Consider the following. In case that the Central Limit Theorem is NOT applicable, enter 0 as your answer. Otherwise, your answer must be in FOUR DECIMAL places. In a town, the mean weight of male adults is 73kg with a standard deviation of 12kg. Suppose that 50 male adults are randomly chosen for a study. What is the probability that their mean weight is greater than 75kg? Suppose that 10 male adults are randomly chosen. What is the probability that their mean weight is between 80kg and 85kg? Assume that the distribution of weights of male adults are normally distributed. A platform has a “safe weight” of 2000kg. In other words, a platform can safely handle weight up to 2000 kg. If 25 randomly chosen male adults are to use the platform at the same time, what is the probability that the platform cannot handle their weight? ,
According to a study, the length of pregnancy has an unknown distribution with a mean of 265 days and a standard deviation of 15.4 days. Let XX be the length of pregnancy for a randomly selected female and let ¯¯¯XX¯ be the average length of pregnancy for a random sample of size 22. 1. Describe the probability distribution of XX and state its parameters μμ and σσ: X∼X∼ ( μ=μ= , σ=σ= ) 2. Explain why the Central Limit Theorem can or can not be applied The Central Limit Theorem for Sample Means be applied because