The Central Limit Theorem (CLT) saysO Samples of size 15 are large enough for the CLT to apply for any populations.O As the sample size increases, the sampling distribution of the mean will get closer and closer to a normal distribution.O Regardless of the sample size, the sampling distribution of the mean is always close to a normal distribution.O Only for symmetric population distributions, the sampling distribution of the mean will get close to a normal distribution as the sample size increases.

Here we have given the question about the central limit theorem. We have to select the one correct…

Answered: The Central Limit Theorem (CLT) says O…

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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An ecologist is studying the impact of local polluted waters on the growth of alligators. The length of adult male alligators typically follows a normal distribution with a standard deviation of 2 feet. The ecologist wants to estimate the mean length of this population of alligators. Suppose she samples n alligators at random and uses the sample mean, X to as an estimator for u. a. What is the bias and variance of the estimator? (Note, these may be a function of n.) b. If n = 4, what is the probability that the estimator is within one foot of the true mean? (I.e. find P(|X – µ| < 1). c. What sample size, n, is required for the estimator to be within one foot of the true mean with 95% probability? (I.e. find the value of n that satisfies P(|X – µ| < 1) = 0.95.) d. Suppose the ecologist ends up sampling n = 9 alligators and calculates a sample mean of ī = 10.4 feet. Construct a 95% confidence interval for the population mean. e. Give an interpretation for the interval obtained in (d).
If a sample size is 84, comes from a population that is normally distributed, and the data is ordinal ranging from 135 to 154, can one say that the data satisfies one of the distribution assumptions for a t-test, namely that the data is ordinal?
Hello what about 3b?
What would happen to the sampling distribution if you increased the size of the samples taken from the population? O The center of the sampling distribution will get further away from the parameter O The spread of the sampling distribution will get larger O The center of the sampling distribution will get closer to the parameter O The spread of the sampling distribution will get smaller
please state the approximate distribution of the sample mean
The heights of fully grown trees of a specific species are normally distributed, with a mean of 68.5 feet and a standard deviation of 6.00 feet. Random samples of size 12 are drawn from the population. Use the central limit theorem to find the mean and standard error of the sampling distribution.
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.
The central limit theorem states that the sampling distribution of sample means has a mean equal to the population -- mean mean mean divided by the population standard deviation mean divided by the population standard deviation standard deviation standard deviation standard deviation divided by the square root of N.
A simple random sample of size n=50 is obtained from a population with a mean of 46 and a standard deviation of 7. Does the population need to be normally distributed for the sampling distribution of x bar to be approximately normally distributed? Why? What is the sampling distribution of x bar?
According to the central limit theorem (CLT), no matter which distribution the data is collected from, as long as some conditions are met, we can always expect the sample average to behave like a normal random variable, i.e., the sampling distribution can be approximated by a normal distribution. Which is NOT a CLT condition for sample mean? Group of answer choices The original distribution of the data is Normal. A random sample with sample size is larger than 30 with no extreme outlier A random sample with sample size is less than 30 with no outliers. The sample size has to be larger than 10.
Consider the distribution of the average number of hours that college students spend sleeping each weeknight. This distribution is very skewed to the right, with a mean of 5 and a standard deviation of 1. A researcher plans to take a simple random sample of 18 college students. If we were to imagine that we could take all possible random samples of size 18 from the population of college students, the sampling distribution of the average number of hours spent sleeping will have a shape that is ☐ Exactly normal. Just like the population (i.e., very skewed to the right). Less skewed than the population.
What is the Central Limit Theorem? It is always true that as the sample size, n, increases, the distribution of the sample means will be approximately normally distributed. Explain

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