An experiment is designed to test a new material being used in the creation of baseball bats. A group of 20 volunteers with baseball-playing experience are recruited to participate in the experiment. Each of the volunteers is randomly assigned a bat made up of either the new material or an existing old material, and hits a ball off a tee 25 times, with the mean distance that the ball travels calculated at the end of the trials. After an appropriate period of rest, the volunteers then use the other bat.
A table summarizing the results of the experiment are shown below:
Histograms summarizing the results are also shown here:
The researchers wish to determine if the new material resulted in the average distance traveled by the batted balls was greater than the average from the old material.
a. For the experiment described above, define the hypotheses that the researcher wishes to test and name test that they should conduct. You do not need to execute the stated test.
b. For the test named in part (a), have the conditions for running the test been met? Explain why or why not.
c. The results of the experiment result in a statistically significant conclusion. Based on the design of the experiment, can the manufacturer conclude that the average distance traveled by batted balls is greater for the new material than the old material, for players similar to those in the experiment? Justify your response.