Chapter 6.5, Problem 2DC

Solution

To Calculate:

The number of resampling choices for treatment and control groups that are theoretically possible.

To Explain:

Suppose that a computer is programmed to generate all possible treatment and control groups, to calculate their difference of means and draw the histogram. Will you prefer to make conclusions about the experiment using the histogram from the computer or the histogram for your class.

  $184756$ is the number of resampling choices possible. The computer generated histogram is preferable.

Given:

There are total $20$ observations which are to be resampled into two groups of $10$ each.

Concepts Used:

The number of ways to select $r$ objects from $n$ distinct objects is ${}_n{C}_r=\frac{n!}{\left(n-r\right)!r!}$ .

Calculations:

Determine the number of ways to select the treatment group, the remaining ten observations will automatically form the control group.

  $\begin{array}{c}{}_{20}{C}_{10}=\frac{20!}{10!10!}\\ =184756\end{array}$

The histogram generated by computer will have 184756 possible resampling choices which will represent the experiment in much more detail as compared to merely 10 resampling choices from the class. So the computer generated histogram is preferable.

Conclusion:

  $184756$ is the number of resampling choices for treatment and control groups that are theoretically possible. The computer generated histogram is preferable.