In Test A, suppose you make 100 experimental measurements of some quantity and then calculate mean, standard deviation, and standard error of the numbers you obtain. In Test B, suppose you make 1000 experimental measurements of the same quantity and you again calculate mean, standard deviation, and standard error. 1) Which of the following statements is the most likely description of the comparison of the standard deviations found in Test A and Test B?
A. The standard deviations found in Test A and Test B will be about the same.
B. The standard deviation found in Test A will about be twice as big as the standard deviation found in Test B.
C. The standard deviation found in Test A will about be four times as big as the standard deviation found in Test B. The standard deviation found in Test B will about be twice as big as the standard deviation found in Test A.
D. The standard deviation found in Test B will about be four times as big as the standard deviation found in Test A.
2) Which of the following statements is the most likely description of the comparison of the standard errors found in Test A and Test B?
A. The standard errors found in Test A and Test B will be about the same.
B. The standard error found in Test A will about be twice as big as the standard error found in Test B.
C. The standard error found in Test A will about be four times as big as the standard error found in Test B.
D. The standard error found in Test B will about be twice as big as the standard error found in Test A.
E. The standard error found in Test B will about be four times as big as the standard error found in Test A.
3) This question and the next one refer to a hypothetical experiment in which you slide red and green blocks down an identical ramp to see how far they go before stopping.
After doing three trials of each case you find that the best estimate of the distance slid by red blocks is 15 + 3 feet and that the best estimate of the distance slid by green blocks is 25 + 4 feet. Find the t' parameter for the comparison of the distance slid by red and green blocks.
a. t' = 2.0
b. t' = 2.5
c. t' = 3.0
d. t' = 3.5
e. t' = 4.0
4) Suppose the experiments described in Question 3 are testing the claim that the distance slid by a block does not depend on the color of the block. Which of the following conclusions regarding this claim is most consistent with your data?
A. The claim is true.
B. The claim is false.
C. The claim might be true or it might be false.