Question

QUESTION 1

1. During the Middle Ages, armies often used catapults to launch flaming projectiles at their enemies. Because of the inferior materials and manufacturing processes of the time, excessive variability in the weight of flaming projectiles could damage the arm of a catapult, thus leading to inaccurate launches. Because of this problem, most armies maintained a staff of quality engineers to inspect projectiles prior to their use. During the Hundred Years’ War, the English army applied the following hypothesis test to each shipment of projectiles they received.

   The English army wanted to have a test power of at least 40% when the true standard deviation of projectile weight was 15 lb. In addition, they used a level of significance of 0.05.

   What is the smallest sample size that the engineers need to use?   (Because it's hard to read the chart exactly, I'll allow a tolerance of +/- 1 on this problem.)

Answer 1

Solution Given that The Tove Jandard deviation of projechile weight Again English Amy wanted to have a test paesco of at least T= 15 lb. = 40% to the Ecooo amount is 60% 60 % of the True Standard deviation o 60* 15*60% 3 1560 - 9 109 30. 620001C-79 goven level of sigrnificance is 0:05 Ao it is an one-toiled test the - toiled test the Z-value at 0.0598 = 1.615. oo Sample size ni Zoo 2 2 e2 = (inGu5j_15) 2-10604 225 (912 81 608.8556 7.516 ~ 8 81 As the sample size must be an integer ce consided n=8 Z *

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