Differences Between Means

Now that we know the ideas behind this problem and how to take trials, we can extend our knowledge to answer our problem by performing more trials. Once we obtain more trials, we can assess whether the helium balls can be kicked farther.

Use the spreadsheet, "Day 4", to answer the following questions and to come to a conclusion about this experiment.

We can run one, ten or a hundred separate trials by clicking on the appropriate button. The spreadsheet will find the difference between the trials, whether it is greater than the absolute difference and keep track of the percentage of trials that were greater.

  1. Generate ten trials. How many of the trials had differences greater than the actual data?
  2. Generate a total of 20 trials. How many of these trials had differences greater than the actual data?
  3. Now, generate fifty trials. What percentage of trials had differences greater than the actual data?
  4. Decide a significant percentage as to whether the helium balls can be kicked farther than the air balls and decide if your trials support or reject the idea that the helium balls can be kicked farther?
  5. What factors do you think contribute to deciding what level of significance is appropriate? For example, if the analyses involved testing medicines for some medical purpose would you want a 1, 5, or 10% level of significance?
  6. Erase the trials and generate 50 new trials. What was the percentage of trials that were greater than the actual difference? How does this percentage compare to the one you found earlier for 50 trials?
  7. Again, erase the trials and generate 50 more. Find the percentage and judge how stable these analyses appear to be in comparison to the other trials you've done. In other words, are you getting percentage close to each other are do they vary greatly?
  8. If the analyses were to vary greatly, would it be appropriate to decide if the difference between the two balls is statistically significant?
  9. Erase the trial, and generate 100 trials. Based on the percentage and an appropriate level of significance (1, 5, 10%, you choose), determine if the helium balls are kicked farther or if the difference can occur randomly?
  10. If someone told you that helium balls can be kicked farther, would you be able to support this statement based on your 100 trial analysis?
  11. If you were to run more and more trials, what do you think this would do to the accuracy of your analysis?

Continue to next section.

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