Nerf guns For a class project, a statistics student tested his theory about the regulators found on Nerf guns: that they slow the muzzle velocity of the darts. He collected three Nerf guns that had 22 barrels among them, each barrel individually regulated. He fired a Nerf dart once using each barrel and measured how many inches it traveled, using the same dart on all tests. He then removed the regulators and fired one shot with each of the barrels again. The data he recorded appears below:
barrel regulator no regulator
1 231 252
2 208 245
3 202 251
4 212 265
5 193 210
6 201 234
7 125 155
8 168 141
9 38 74
10 154 231
11 122 103
12 77 123
13 243 262
14 215 252
15 239 221
16 234 268
17 232 245
18 237 252
19 230 254
20 245 259
21 218 249
22 246 262
a) Is this an observational study or an experiment?
b) If there is no difference between firing with and without a regulator, what percentage of all barrels would expect to fire a Nerf dart further without a regulator than with a regulator?
c) How many barrels actually fired further without a regulator?
d) Assuming that there really is no difference between using a regulator and not using a regulator, compute the probability of observing a result at least as extreme as the one observed here?
e) Are the results of this study unlikely to be observed by chance?
f) What can you conclude about the student’s original question?
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