The Central Limit Theorem is important in statistics because a) for a large n, i
ID: 3217554 • Letter: T
Question
The Central Limit Theorem is important in statistics because a) for a large n, it says the population is approximately normal. b) for any population, it says the sampling distribution of the sample mean is approximately normal, regardless of the sample size. c) for a large n, it says the sampling distribution of the sample mean is approximately normal, regardless of the shape of the population. d) for any sized sample, it says the sampling distribution of the sample mean is approximately normal. For air travelers, one of the biggest complaints is of the waiting time between when the airplane taxis away from the terminal until the flight takes off. This waiting time is known to have a right skewed distribution with a mean of 10 minutes and a standard deviation of 8 minutes. Suppose 100 flights have been randomly sampled. Describe the sampling distribution of the mean waiting time between when the airplane taxis away from the terminal until the flight takes off for these 100 flights. a) Distribution is right skewed with mean = 10 minutes and standard error = 0.8 minutes. b) Distribution is right skewed with mean = 10 minutes and standard error = 8 minutes. c) Distribution is approximately normal with mean = 10 minutes and standard error = 0.8 minutes. d) Distribution is approximately normal with mean = 10 minutes and standard error = 8 minutes. Which of the following statements about the sampling distribution of the sample mean is incorrect? a) The sampling distribution of the sample mean is approximately normal whenever the sample size is sufficiently large (n greaterthanorequalto 30). b) The sampling distribution of the sample mean is generated by repeatedly taking samples of size n and computing the sample means. c) The mean of the sampling distribution of the sample mean is equal to mu. d) The standard deviation of the sampling distribution of the sample mean is equal to sigma. Which of the following is true about the sampling distribution of the sample mean? a) The mean of the sampling distribution is always mu. b) The standard deviation of the sampling distribution is always sigma. c) The shape of the sampling distribution is always approximately normal. d) All of the above are true.Explanation / Answer
28.
Option "c"
Explanation: The Central Limit Theorem tells us that with a large enough sample, most of the sample means will be close to the population mean. Given a population with a finite mean and a finite non-zero variance 2, the sampling distribution of the mean approaches a normal distribution with a mean of and a variance of 2/N as N, the sample size, increases.