Question 3 The central limit theorem states that for a sufficiently large sample

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Question 3

The central limit theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to 2 and the variance equal to 2/n.

True

False

Question 5

For the sampling distribution of sample means, sampling error will decrease as sample size increases.

True

False

Question 8

Sampling error is defined as _________.

/n

N - n

Question 9

The size of the sampling error is ________.

Directly related to the sample size—in other words, the larger the sample size, the larger the sampling error

Directly related to the population mean—in other words, the larger the mean, the larger the sampling error

Inversely related to the sample size—in other words, the larger the sample size, the smaller the sampling error

Inversely related to the population standard deviation—in other words, the smaller the standard deviation, the larger the sampling error

Question 15

Bones Brothers & Associates prepare individual tax returns. Over prior years, Bones Brothers has maintained careful records regarding the time to prepare a return. The mean time to prepare a return is 90 minutes and the standard deviation of this distribution is 14 minutes. Suppose 100 returns from this year are selected and analyzed regarding the preparation time. What assumptions do you need to make about the shape of the population distribution of all possible tax preparation times to make inferences about the mean time to complete a tax form?

The population distribution is skewed to the right.

The population distribution is skewed to the left.

The population distribution is normal.

The shape of the population distribution does not matter.

/n

N - n

Explanation / Answer

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3)

The central limit theorem states that for a sufficiently large sample the sampling distribution of the means of all possible samples of size n generated from the population will be approximately normally distributed with the mean of the sampling distribution equal to 2 and the variance equal to 2/n.

Ans: False

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.

The central limit theorem tells us that for a population with a mean µ and a finite variance 2, 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 2/n, no matter the distribution of the population, assuming a large sample size.

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