In your attempt to “catch them all†you hunt the prized Pokemon,Mew and Mewtwo. As you battle them with your top 25 Pokemon, youlose every battle. However, after each battle, you notice that thehit points (HP) of Mew and Mewtwo have been reduced. The remainingHPs of Mew and Mewtwo are shown below after battling yourrespective Pokemon. (A higher HP remaining indicates more successin battle.) You suspect that Mewtwo is the tougher opponent, andyou want to test this hypothesis at the 95% level ofconfidence.
Attacker | Mew | Mewtwo |
Bulbasaur | 402 | 377 |
Ivysaur | 305 | 354 |
Venusaur | 348 | 343 |
Charmander | 350 | 341 |
Charmeleon | 320 | 347 |
Charizard | 340 | 401 |
Squirtle | 396 | 406 |
Wartortle | 311 | 364 |
Blastoise | 367 | 381 |
Caterpie | 309 | 402 |
Metapod | 391 | 387 |
Butterfree | 385 | 347 |
Weedle | 390 | 349 |
Kakuna | 313 | 402 |
Beedrill | 396 | 403 |
Pidgey | 394 | 389 |
Pidgeotto | 329 | 395 |
Pidgeot | 375 | 356 |
Rattata | 364 | 340 |
Raticate | 340 | 400 |
Spearow | 365 | 405 |
Fearow | 395 | 402 |
Ekans | 365 | 377 |
Arbok | 396 | 341 |
Pikachu | 381 | 399 |
Assume that before each battle, Mew and Mewtwo started with thesame number of HPs.
a. State the null hypotheses for this test.
b. State the alternative hypotheses for this test.
c. What type of test will you use to test this hypothesis?
d. Describe the Type I Error for this test, and explain itsimplication for you as you continue your quest.
e. Describe the Type II Error for this test, and explain itsimplication for you as you continue your quest.
f. What is the rejection region for this hypothesis test?
g. Calculate the test statistic for this hypothesis test. Whatis your conclusion?
h. If you reject the null hypothesis for this test, what is theprobability that you have committed a Type I Error? (i.e., find thep-value for this test.)
i. What action will you take as you continue your quest based onyour conclusion.
