The central limit theorem proposes that: The distribution of sample means will be approximately normal in shape only if the underlying population distribution is normal and provided that sample sizes are large enough (i.e., N = 30 or greater) The distribution of sample means will be approximately normal in shape only if the original sample distribution was normal The mean of any given sample will approximately equal the population mean The distribution of sample means will be approximately normal regardless of the original sample distribution shape, provided sample sizes are large enough (i.e., N = 30 or greater)

Introduction: It is required to identify the correct statement regarding the central limit theorem.

Answered: The central limit theorem proposes…

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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Fill in the blanks please. a) It is often the case in practical applications that a normality assumption is not tenable. In these circumstances, it is desirable to base inference on tests that are valid over a wide range of distributions of the parent population. Such tests are called .............................. tests b) Of all possible estimators of α and β that are linear in the Yi and unbiased, the least squares estimators that have the smallest variances are said to be………………………….…………….……………………………. according to the …..………………………..……………… theorem thanks
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, μ, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate μ. Assuming that the standard deviation of the population of shopping times at the supermarkets is 26 minutes, what is the minimum sample size she must collect in order for her to be 90%confident that her estimate is within 5 minutes of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
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.
What does the Central Limit Theorem tell about the sample mean? If the sample size is large, the distribution of all individual observations should be normally distributed. If your sample size is large, the distribution of the sample mean should be normally distributed with the population mean as its center. The distribution of the sample mean is always perfectly normally distributed. O If your sample size is large, the distribution of the population mean should be normally distributed with the population mean as its center.
Test of independence is considered a distribution-free test because: Select one: a. It requires the population to follow a chi-square distribution b. It requires the population to follow a certain distribution c. It does not require the population to follow a certain distribution d. It requires the population to be normally distributed In a uniform goodness of fit test, we assume that: Select one: a. None of the answers is correct b. Every value has the same chance of occurrence c. Every value has a different chance of occurrence d. Values can either have the same chance or different chance of occurrence
Inferential statistical analyses that are not based on a set of assumptions of the z test? a. Permissible only when certain assumptions about the sample are met b. nonparametric c. parametric d. innacurate
Executives of a supermarket chain are interested in the amount of time that customers spend in the stores during shopping trips. The executives hire a statistical consultant and ask her to determine the mean shopping time, μ, of customers at the supermarkets. The consultant will collect a random sample of shopping times at the supermarkets and use the mean of these shopping times to estimate μ. Assuming that the standard deviation of the population of shopping times at the supermarkets is 27 minutes, what is the minimum sample size she must collect in order for her to be 95% confident that her estimate is within 5 minutes of μ? Carry your intermediate computations to at least three decimal places. Write your answer as a whole number (and make sure that it is the minimum whole number that satisfies the requirements).
5
An estimator that tends to produce more accurate estimates of the population parameter as the sample size increases is best characterized as a(n)_____________Select one: A. A consistent estimator approaches the estimated population parameter as the sample size grows larger. B. An unbiased estimator is consistent if its standard error is lower than that of other estimators of the estimated population parameter. C. An estimator is consistent if its expected value equals the estimated population parameter. D. An estimator is consistent if it always gives the correct value of the estimated population parameter.
A random sample of size 10 yielded roughly "mound-shaped" data with a sample mean of 63.5 and a sample variance of 60.8. Let (L, OU) be the interval estimate that contains the population mean with 95% probability. Find the width of the interval. That is, find 0 – 0₁. 4.52 5.49 5.58 5.70 9.04 10.99 11.16 11.40 none of the other answers give the correct width

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		The distribution of sample means will be approximately normal in shape only if the underlying population distribution is normal and provided that sample sizes are large enough (i.e., N = 30 or greater)
		The distribution of sample means will be approximately normal in shape only if the original sample distribution was normal
		The mean of any given sample will approximately equal the population mean
		The distribution of sample means will be approximately normal regardless of the original sample distribution shape, provided sample sizes are large enough (i.e., N = 30 or greater)