Question

b. write each yield measurement from the table on an equal - sized piece of paper. place the pieces of paper in a bag, shake, and randomly choose 10 pieces of paper. call this the “control” group, and call the 10 pieces in the bag the “treatment” group. then repeat part (a) and return the pieces to the bag. perform this resampling experiment five times.
c. how does the difference in the means of the control and treatment groups compare with the differences resulting from chance?

Explanation:

This problem involves analyzing the difference in means between control and treatment groups from a resampling experiment. In statistical analysis (subfield of Mathematics), when we perform resampling (like the bag - and - paper experiment here), the differences in means from chance (the resampling experiments) help us understand if the original difference between control and treatment is significant. If the original difference in means is much larger (or smaller, depending on the context) than most of the differences from the resampling (chance - based) experiments, it suggests that the original difference is not just due to chance. If it's within the range of the chance - based differences, then chance could be a plausible explanation.

Answer:

To determine how the difference in the means of the control and treatment groups compares with the differences resulting from chance, we first calculate the difference in means for the original control and treatment groups. Then, we calculate the differences in means for each of the five resampling (chance - based) experiments. We then compare the original difference to the distribution of the chance - based differences. If the original difference is outside the range of most (e.g., 95% or a pre - determined threshold) of the chance - based differences, we can say it is unlikely to be due to chance. If it is within the range of the chance - based differences, it is likely that chance could explain the difference. (The specific comparison depends on the actual numerical values from the experiments, but this is the general method of comparison.)