Question

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.

How would you expect the mean, standard deviation, and standard errors found in Test A and Test B to compare? (You can use the Excel simulation and change the "Number of Experiments" parameter to investigate this yourself. The calculations of mean, standard deviation, and standard error are shown in red at the top of the Excel page).

A.) I would expect the means, the standard deviations, and the standard errors in Test A and Test B to be about the same.

B.) I would expect the means of the two tests to be about the same, but both the standard deviation and the standard error in Test B should be smaller than in Test A

C.) I would expect the means of the two tests to be about the same, but both the standard deviation and the standard error in Test B should be bigger than in Test A

D.) I would expect the means and standard deviations in the two test to be about the same, but the standard error in Test B should be smaller than in Test A.

E.) would expect the means and standard deviations in the two test to be about the same, but the standard error in Test B should be larger than in Test A.

Answer 1

Since we are measuring the same quantity 100 times and 1000 times respectively in both the tests, we would expect the means and standard deviations to not be significantly different from each other.
The standard errors would differ, though, since the formula is = standard deviation/square root of sample size. Since the sample sizes of both the tests are so significantly different, the corresponding standard errors will also be significantly different! More specifically, the standard error of Test B will be smaller than that of Test A.
Hence, our answer is: I would expect the means and standard deviations in the two tests to be about the same, but the standard error in Test B should be smaller than in Test A.