Question

A. The Train Station has a database of travel times on the blue line ever sense it began running. An analyst pulls a report of all the travel times from the Washington stop to the Oak Park stop. The average is 14 and the standard deviation is 4.

B. The analyst calculates 81 average travel times based on a random sample of 49 travel times in each sample. A subset of these averages is 14.5, 16.8, 17.2, etc.

C. One of the sets of 49 travel times has values such as 12, 14, 18, 17, etc.

Question 1

Indicate which of the three is a sample distribution

Choice A

Choice B

Choice C

Question 2

Indicate which of the three is the population distribution

Choice A

Choice B

Choice C

Question 3

Indicate which of the three is a sampling distribution

Choice A

Choice B

Choice C

Question 4

According to the Central Limit Theorem (and only the Central Limit Theorem) what will be the average of the sampling distribution

A) 14

B) 4/2

C) 14/81

D) 4/7

Question 5

According to the Central Limit Theorem (and only the Central Limit Theorem) what will be the standard deviation of the sampling distribution

A) 14

B) 4/6

C) 14/10

D) 4/7

Question 6

According to the Central Limit Theorem (and only the Central Limit Theorem) what will be the shape of the sampling distribution

A) Regular

B) Normal

C) Non-normal

D) Rectangular

Question 7

Now suppose that the analyst calculates 100 averages each with a random set of 36 travel times in each sample. What will be the standard deviation of the sampling distribution. All other facts are the same.

A) 14

B) 4/6

C) 14/10

D) 4/7

Question 8

Which of the two sampling distributions will have a WIDER spread?

A) The first

B) The second

Answer 1

Solution:

Question 1

Indicate which of the three is a sample distribution

Choice C

Because C is just one sample of 49 samples

Question 2

Indicate which of the three is the population distribution

Choice A

Because A based on the entire data available

Question 3

Indicate which of the three is a sampling distribution

Choice B

Because it is based on the various samples taken from the population

Question 4

According to the Central Limit Theorem (and only the Central Limit Theorem) what will be the average of the sampling distribution

A) 14

Question 5

According to the Central Limit Theorem (and only the Central Limit Theorem) what will be the standard deviation of the sampling distribution

D) 4/7

Question 6

According to the Central Limit Theorem (and only the Central Limit Theorem) what will be the shape of the sampling distribution

B) Normal

According to the central limit theorem, if sufficiently large (>30) random sample is taken from the population, then the distribution of the sample means will be approximately normally distributed.

Question 7

Now suppose that the analyst calculates 100 averages each with a random set of 36 travel times in each sample. What will be the standard deviation of the sampling distribution. All other facts are the same.

B) 4/6

Question 8

Which of the two sampling distributions will have a WIDER spread?

B) The second

​​​​​​​Because the standard error of second is more than the standard error of first