Ch 17

Question 1

What does the Central Limit Theorem state?

Answer 1

The Central Limit Theorem states that the distribution of the sample means approaches a normal distribution as the sample size increases, regardless of the population’s distribution.

Question 2

True or False: The Central Limit Theorem applies only to normally distributed populations.

Answer 2

False

Question 3

Fill in the blank: The Central Limit Theorem is important because it allows us to use __________ methods to make inferences about population parameters.

Answer 3

normal

Question 4

What is the minimum sample size typically required for the Central Limit Theorem to apply?

Answer 4

30

Question 5

Multiple Choice: Which of the following scenarios demonstrates the Central Limit Theorem? A) Sampling from a uniform distribution, B) Sampling from a normal distribution, C) Both A and B

Answer 5

C) Both A and B

Question 6

What happens to the shape of the sampling distribution as the sample size increases?

Answer 6

It becomes more normally distributed.

Question 7

True or False: The mean of the sampling distribution is equal to the population mean.

Answer 7

True

Question 8

Fill in the blank: The standard deviation of the sampling distribution is known as the __________.

Answer 8

standard error

Question 9

What is the formula for calculating the standard error?

Answer 9

Standard Error = Population Standard Deviation / √n

Question 10

Multiple Choice: If a population has a mean of 50 and a standard deviation of 10, what is the standard error for a sample size of 25? A) 2, B) 4, C) 10

Answer 10

A) 2

Question 11

What is the impact of increasing the sample size on the standard error?

Answer 11

The standard error decreases.

Question 12

True or False: The Central Limit Theorem applies to samples drawn from any population distribution.

Answer 12

True

Question 13

Fill in the blank: The Central Limit Theorem allows statisticians to use the __________ distribution to make inferences about population parameters.

Answer 13

normal

Question 14

What is the significance of the Central Limit Theorem in hypothesis testing?

Answer 14

It allows for the use of normal distribution to determine probabilities and make decisions about hypotheses.

Question 15

Multiple Choice: Which of the following is NOT a condition for the Central Limit Theorem? A) Random sampling, B) Sample size must be large enough, C) Population must be normally distributed

Answer 15

C) Population must be normally distributed

Question 16

What is the effect of skewness in the population distribution on the sample means as the sample size increases?

Answer 16

The sample means will still tend to be normally distributed regardless of skewness.

Question 17

True or False: The Central Limit Theorem can be applied to proportions as well as means.

Answer 17

True

Question 18

Fill in the blank: In the context of proportions, the Central Limit Theorem applies when np and n(1-p) are both greater than __________.

Answer 18

5

Question 19

What does ‘n’ represent in the context of the Central Limit Theorem?

Answer 19

The sample size

Question 20

Multiple Choice: Which of the following best describes the Central Limit Theorem? A) The mean of a population is always normal, B) The mean of a sample is always normal, C) The distribution of sample means approaches normality as sample size increases

Answer 20

C) The distribution of sample means approaches normality as sample size increases

Question 21

What is one practical application of the Central Limit Theorem in statistics?

Answer 21

It is used to construct confidence intervals for population parameters.

Question 22

True or False: The Central Limit Theorem guarantees that all sample means will be exactly equal to the population mean.

Answer 22

False

Question 23

Fill in the blank: The Central Limit Theorem is foundational for __________ statistics.

Answer 23

inferential