Question

Suppose you are measuring the stopping distance (how long it takes to go from 60mph to 0mph) of cars made by a certain manufacturer. Let's assume that the car manufacturers' claims are correct and that, for all cars made by them, the average is 4500 milliseconds with standard deviation 1050 milliseconds.
You sample 25 cars and get a sample average of 4700 seconds.
The Central Limit Theorem tells us that if we repeatedly take new random samples of this size from this distribution and calculate the average each time, then:

a. The sample averages should be centered around ?
b. The standard deviation of the sample averages (called  --- deviation error standard variation standard error variation error ) would be ___
c. If you took a new sample with a larger sample size you would expect: ?

1. the sample average to be farther from 4500

2. the sample average to be closer to 4700    

3. the sample average to be closer to 4500

4. the sample average to be exactly equal to 4700

5. the sample average to be exactly equal to 4500

Answer 1

Suppose you are measuring the stopping distance (how long it takes to go from 60mph to 0mph) of cars made by a certain manufacturer. Let's assume that the car manufacturers' claims are correct and that, for all cars made by them, the average is 4500 milliseconds with standard deviation 1050 milliseconds.
You sample 25 cars and get a sample average of 4700 seconds.
The Central Limit Theorem tells us that if we repeatedly take new random samples of this size from this distribution and calculate the average each time, then:

a. The sample averages should be centered around 4700
b. The standard deviation of the sample averages (called  --- deviation error standard variation standard error variation error ) would be   = 210
c. If you took a new sample with a larger sample size you would expect: ?

3. the sample average to be closer to 4500