Question 242697: 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
246
319
412
315
385
332
298
377
285
347
365
396
430
385
461
419
400
321
406
275
311
State the appropriate null and alternative hypotheses.
Calculate the test statistic.
At an alpha=0.01, should Coach Juarez reject the null hypothesis?
Assuming the starting lineup is a representative sample, what conclusions can the coach draw?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! 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
246
319
412
315
385
332
298
377
285
347
365
396
430
385
461
419
400
321
406
275
311
State the appropriate null and alternative hypotheses.
Ho: u = 312
H1: u > 312 (Coaches desire)
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Calculate the test statistic.
Find the mean and standard deviation of the sample of the 22 players.
Let's say the numbers are 320 and 20 (that's a guess)
Find the t-value of 320 = (320-312)/[20/sqrt(22)] = 1.8762
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At an alpha=0.01, should Coach Juarez reject the null hypothesis?
Find the critical valu for a right-tail test with alpha = 1% and
df = 21: t = 2.5176
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Conclusion: Since the test stat is not in the reject interval,
do not reject Ho.
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Assuming the starting lineup is a representative sample, what conclusions can the coach draw?
The players need to build more muscle power.
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Cheers,
Stan H.
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