A company that manufactures steel wires guarantees that , the mean breaking stre

Question

A company that manufactures steel wires guarantees that , the mean breaking strength (in kilonewtons) of the wires is greater than 50. The quality control inspector takes a sample of wires and measures their strength to test Ho : = 50 versus Ha : > 50 If Type I error is made, what conclusion was drawn regarding the mean breaking strength? a. b. Describe consequences of Type I error in this situation. c. If Type II error is made, what conclusion was drawn regarding the mean breaking strength? Describe consequences of Type II error in this situation. This test uses one-tailed alternate hypothesis. Explain why a one-tailed hypothesis is more appropriate than a two-tailed hypothesis in this situation. d. e.

Explanation / Answer

a) A type I error is made when the null hypothesis is rejected even when it is true. Therefore in this case we would conclude in case of type I error that the mean strength is greater than 50 even though it is not greater than 50.

b) The consequences here could be fatal as the mean strength of the wire is in reality less than or equal to 50 but if we conclude that it is greater than 50 and we use it accordingly giving it force of greater than 50 then it may lead to a calamity

c) Type II error is committed when the null hypothesis is retained even though it is false. Here it would mean that we will conclude that the wire has strength equal to 50 , not greater than 50 even though in reality it has a strength greater than 50

d) Here the type II error wont have as drastic consequences as the type I error because lesser load will be given to the wire as we concluded it has a lower mean strength although the real strength would be higher.

e) This is a one tailed test, because we only are interested in measuring whether it is safe for load and therefore has a higher strength ( higher than 50 )

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