Question: The players on last year’s football team at State College were able to bench press a mean of 312 lb. Coach Juarez made it clear to the players during spring training that the team’s average best lift had to improve. A special weight-training program was launched, and all the players participated. In an effort to measure the team’s progress, the coach recorded the heaviest lifts of the starting offensive and defensive lineups at the start of this season. Results are as follows:

346 412 332 285 396 461 321 275

246 315 298 347 430 419 406 311

319 385 377 365 385 400

a. State the appropriate null and alternative hypotheses.

b. Calculate the test statistic.

HINT sample mean=356.43 lb

Sample standard deviation = 56.05 lb

c. At a = 0.01, should Coach Juarez reject the null hypothesis?

d. Assuming the starting lineup is a representative sample, what conclusion can the coach draw?