答案和详解如下： 1.The central limit theorem concerns the sampling distribution of the: A) population mean. B) sample mean. C) sample standard deviation. D) population standard deviation. The correct answer was B) 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. 2.According to the Central Limit Theorem, the distribution of the sample means is approximately normal if: A) the underlying population is normal. B) the sample size n>30. C) the standard deviation of the population is known. D) the population contains at least 100 samples. The correct answer was B) 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. 3.The Central Limit Theorem states that, for any distribution, as n gets larger, the sampling distribution: A) becomes larger. B) becomes smaller. C) approaches a normal distribution. D) approaches the mean. The correct answer was C) As n gets larger, the variance of the distribution of sample means is reduced, and the distribution of sample means approximates a normal distribution. 4.All of the following are predictions of the central limit theorem EXCEPT the: A) mean of the sampling distribution of the sample means will be equal to the population mean. B) sampling distribution of sample means will be approximately normal if the sample size is sufficiently large. C) standard error of the sample mean will increase as the sample size increases. D) variance of the sampling distribution of sample means will approach the population variance divided by the sample size. The correct answer was C) 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 three choices are predictions of the central limit theorem. 5.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) an approximately normal distribution, because the sample is greater than 300. D) any probability distribution. The correct answer was D) 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. 6.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/n. B) 16.62/√n. C) indeterminate for sample with n<30. D) 16.62. The correct answer was D) 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. | 
发表于 2008-4-14 14:27
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