An automobile manufacturer is considering using robots for part of its assembly

Question

An automobile manufacturer is considering using robots for part of its assembly process. Concerting robots is an expensive process, so it will be undertaken only if there is strong evidence hat the proportion of defective installations is lower for the robots than for human assemblers. Let p dent the proportion of defective installations for the robots. It is known that human assemblers have a defect proportion of .02.

a. which of the foloowing pairs of gypotheses should the manufacturer test:

  H0: p = .02 versus Ha: p < .02

or

  H0: p  = .02 versus, Ha: p > .02

explain your answer.

b. In the context of this exercis, describe Type 1 and Type 2 errors.

c. Would you prefer a test with = .01 or = .1? Explain your reasoning

Explanation / Answer

(a)

The manufacturee should test whether the proportion of defective installations for the robots is greater than human assemblers a defect proportion of .02. So hypotheses are:

H0: p  = .02 versus, Ha: p > .02

(b)

Type 1 error:

The manufacture incorrectly conclude that the proportion of defective installations for the robots is greater than 0.02 while actually it is 0.02.

Type II error:

The manufacture incorrectly conclude that the proportion of defective installations for the robots is not greater than 0.02 while actually it is greater than 0.02.

(c)

We prefer = .1 becuase very low level of siginificnace will decrease the probability of rejecting null hypothesis. And in the given case it is better to made to made type 1 error in comaprison to type II error.

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