Reading 10: Sampling and Estimation-LOS d 习题精选 2011, describe, central, center

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Session 3: Quantitative Methods: Application
Reading 10: Sampling and Estimation

LOS d: Interpret the central limit theorem and describe its importance.

 

 

If the true mean of a population is 16.62, according to the central limit theorem, the mean of the distribution of sample means, for all possible sample sizes n will be:

A) 16.62.

B) 16.62 / √n.

C) indeterminate for sample with n < 30.

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According to the central limit theorem, the mean of the distribution of sample means will be equal to the population mean. n > 30 is only required for distributions of sample means to approach normal distribution.

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Suppose the mean debt/equity ratio of the population of all banks in the United States is 20 and the population variance is 25. A banking industry analyst uses a computer program to select a random sample of 50 banks from this population and compute the sample mean. The program repeats this exercise 1000 times and computes the sample mean each time. According to the central limit theorem, the sampling distribution of the 1000 sample means will be approximately normal if the population of bank debt/equity ratios has:

A) a normal distribution, because the sample is random.

B) a Student's t-distribution, because the sample size is greater than 30.

C) any probability distribution.

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The central limit theorem tells us that for a population with a mean μ and a finite variance σ², the sampling distribution of the sample means of all possible samples of size n will be approximately normally distributed with a mean equal to μ and a variance equal to σ²/n, no matter the distribution of the population, assuming a large sample size.

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Which of the following is NOT a prediction of the central limit theorem?

A) The variance of the sampling distribution of sample means will approach the population variance divided by the sample size.

B) The mean of the sampling distribution of the sample means will be equal to the population mean.

C) The standard error of the sample mean will increase as the sample size increases.

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The standard error of the sample mean is equal to the sample standard deviation divided by the square root of the sample size. As the sample size increases, this ratio decreases. The other two choices are predictions of the central limit theorem.

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The central limit theorem states that, for any distribution, as n gets larger, the sampling distribution:

A) approaches a normal distribution.

B) becomes larger.

C) approaches the mean.

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As n gets larger, the variance of the distribution of sample means is reduced, and the distribution of sample means approximates a normal distribution.

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According to the Central Limit Theorem, the distribution of the sample means is approximately normal if:

A) the sample size n > 30.

B) the underlying population is normal.

C) the standard deviation of the population is known.

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The Central Limit Theorem states that if the sample size is sufficiently large (i.e. greater than 30) the sampling distribution of the sample means will be approximately normal.

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The central limit theorem concerns the sampling distribution of the:

A) sample mean.

B) sample standard deviation.

C) population mean.

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The central limit theorem tells us that for a population with a mean m and a finite variance σ², the sampling distribution of the sample means of all possible samples of size n will approach a normal distribution with a mean equal to m and a variance equal to σ² / n as n gets large.

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Which of the following statements regarding the central limit theorem (CLT) is least accurate? The CLT:

A) gives the variance of the distribution of sample means as σ2 / n, where σ2 is the population variance and n is the sample size.

B) holds for any population distribution, assuming a large sample size.

C) states that for a population with mean μ and variance σ2, the sampling distribution of the sample means for any sample of size n will be approximately normally distributed.

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This question is asking you to select the inaccurate statement. The CLT states that for a population with mean μ and a finite variance σ², the sampling distribution of the sample means becomes approximately normally distributed as the sample size becomes large. The other statements are accurate.