Can students throw a baseball farther than a softball? To find out, researchers conducted a study involving 24 randomly selected students from a large high school. After warming up, each student threw a baseball as far as he or she could and threw a softball as far as he she could, in a random order. The distance in yards for each throw was recorded. Here are the data, along with the difference (Baseball – Softball) in distance thrown, for each student:

a. Explain why these are paired data.

b. A boxplot of the differences is shown. Explain how the graph gives some evidence that students like these can throw a baseball farther than a softball.

c. State appropriate hypotheses for performing a test about the true mean difference. Be sure to define any parameter(s) you use.

d. Explain why the Normal/Large Sample condition is not met in this case.

The mean difference  in distance thrown for these 24 students is  yards. Is this a surprisinglylarge result if the null hypothesis is true? To find out, we can perform a simulation assuming that students have the same ability to throw a baseball and a softball. For each student, write the two distances thrown on different note cards. Shuffle the two cards and designate one distance to baseball and one distance to softball. Then subtract the two distances  . Do this for all the students and find the simulated mean difference. Repeat many times. Here are the results of 100 trials of this simulation:

e. Use the results of the simulation to estimate the P-value. What conclusion would you draw?

Transcribed Image Text:

Student Baseball Softball Difference (Baseball – Softball) 65 57 90 58 32 75 66 4 73 61 12 79 65 14 68 56 12 7 58 53 5 41 41 56 44 12 10 70 65 5 11 64 57 7 12 62 60 2 13 73 55 18 14 50 53 -3 15 63 54 16 48 42 17 34 32 2 18 49 48 1 19 48 45 20 68 67 1 21 30 27 3. 22 26 25 1 23 28 25 3 24 26 31 -5 1.