9.4 Under the current manufacturing process, the proportion of computer chips th

Question

9.4 Under the current manufacturing process, the proportion of computer chips that are defective is 0.4 and a new process is claimed to reduce that proportion. It is desired to test this claim statistically. (a) Define the parameter upon which the hypotheses should be based and state the null and alternative hypotheses in terms of this parameter. (b) In this situation, what specifically is a type I error and what are the practical consequences of a type I error? (c) In this situation, what specifically is a type II error and what are the practical consequences of a type II error? X, the number of defective chips in a random sample of n = 20 chips made by the new process, is the test statistic. (d) Which of the following is a reasonable critical region for this testing situation? (i) C = {0, 1, . . . , 5}, (ii) C = {12, 13, . . . , 20}, (iii) C = {0, 1, . . ., 5, 12, 13, . . . ,20}?

Explanation / Answer

(a) Define the parameter upon which the hypotheses should be based and state the null and alternative hypotheses in terms of this parameter.

paratemer : proportion of defectives

(b) In this situation, what specifically is a type I error and what are the practical consequences of a type I error?

type I error will be reject that the proportion of defective is 0.4 when in fact is 0.4

consequences : we could loose more money because the proportion is greater than that

(c) In this situation, what specifically is a type II error and what are the practical consequences of a type II error?

type II error we fail to reject Ho ( proportion of defective is 0.4) when is not 0.4

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