) Which of the following descriptions does NOT illustrate the Central Limit Theorem? A. The Central Limit Theorem is used to approximate the distribution of the sample mean over the distribution of the population mean. B. If the sample size n, where n is sufficiently large is drawn from any population with mean ? and a standard deviation ?, then the sampling distribution of sample means approximates a normal distribution. c. Whenever the population is not normally distributed, or if we do not know distribution, the Central Limit Theorem allows us to conclude that the distribution of sample means will be normal if the sample size is sufficiently large. D. Given a random variable X with mean ? and variance ? 2, then regardless of whether the population distribution of X is normally distributed or not, the shape of the distribution of the sample means taken from the population approaches a normal distribution.
CHOOSE THE CORRECT ANSWER
1.) Which of the following descriptions does NOT illustrate the Central Limit Theorem?
A. The Central Limit Theorem is used to approximate the distribution of the sample mean over the distribution of the population mean.
B. If the
c. Whenever the population is not
D. Given a random variable X with mean ? and variance ? 2, then regardless of whether the population distribution of X is normally distributed or not, the shape of the distribution of the sample means taken from the population approaches a normal distribution.
2.) Which of the following statements is NOT true about Central Limit Theorem?
A. The population mean and the mean of the sampling distribution of the mean are equal.
B. The variance of the sampling distribution of the mean and the population variance is exactly the same.
C. The central limit theorem tells us exactly what the shape of the distribution of the mean will be when we draw repeated samples from a given population.
D. If you take repeatedly independent random samples of size n from any population, then when n is large, the distribution of the sample mean will approach a normal distribution.
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