The expected value of equals the mean of the population from which the sample is drawn _____.

Question

The expected value of  equals the mean of the population from which the sample is drawn _____.

BlackTom AI · Accepted Answer

The question asks about the expected value of x-bar (the sample mean) and how it relates to the population mean. 
Option 1: 'for any sample size' — This is the correct concept: the sample mean is an unbiased estimator of the population mean, so its expected value equals the population mean for any sample size n, assuming random sampling from the population. 
Option 2: 'only if the sample size is 30 or greater' — This is incorrect. There is no requirement that n ≥ 30 for the expected value of the sample mean to equal the population mean. The unbiasedness of x-bar does not depend on a minimum sample size. 
Option 3: 'only if the sample size is 50 or greater' — Similar to option 2, this imposes an arbitrary threshold that does not affect the fundamental property of the estimator. The equality holds for all sample sizes, not just large ones. 
Option 4: 'only if the sample size is 100 or greater' — This is also incorrect for the same reason; the expectation does not depend on such a threshold and applies to any n. 
In summary, the foundational idea is that the sample mean is an unbiased estimator of the population mean, so its expected value matches the population mean regardless of how large or small the sample is.

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The expected value of equals the mean of the population from which the sample is drawn _____.

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The expected value of equals the mean of the population from which the sample is drawn _____.

查看解析

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类似问题

Random samples of size 49 are taken from a population that has 200 elements, a mean of 180, and a variance of 169. The distribution of the population is unknown. The mean and the standard error of the distribution of sample means are _____.

Suppose the weekly salaries of elementary school teachers in GA are normally distributed with a mean of $871 and a standard deviation of $82. What is the probability (P) that the mean salary of 40 elementary school teachers is higher than $953 a week?

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The mean expenditure at a tyre store is $85.00, with a population standard deviation of $9.00. From a random sample of 60 customers, what is the probability that the sample average sale per customer will be between $83 and $86?

Suppose that during any hour in a large department store, the average number of shoppers is 448, with a standard deviation of 21 shoppers. 2. What is the probability that a random sample of 49 different shopping hours will yield a sample mean between 441 and 446 shoppers?

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