9.1 Under the current manufacturing process, the proportion of computer chips th
ID: 3314687 • Letter: 9
Question
9.1 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}?
9.2 Consider the testing situation in problem 9.1, n = 20, and X defined there. Let C = {0, 1, . . ., 5}.
(a) Compute OC(p) for p = .2, .3, .4, .5, .6 and .7 and sketch OC(p).
(b) Compute .
(c) Compute (.2) (d)ForC={0,1,...,k},find k to make as close to 0.05 as possible in the situation.
I only need the answer to 9.2, but want all the information to 9.1 to be available.
Explanation / Answer
Since the claim is that proportion of defective item is less than 0.4,
parameter upon which the hypotheses should be based is 0.4 .
the hypothesis :
Ho: p >= 0.4
H1: p < 0.4
b.
Type I error :
rejecting Ho when it is true.
that means we are accepting the claim of the new technique (number of defective chio is less than 0.4 )when acually there is no sufficient evidence for it .
c.
Type II error:
accepting Ho when it is actually false.
that means, we are rejecting the claim of new technique (number of defective chio is less than 0.4 ) when there is sufficient evidence for it.
n=20, number of defective chip from sample is X.
test statistics = (X-0.4) / sqrt [ {0.4 (1-0.4)} / 20 ]
= (X-0.4) / 0.109545
d. Since it is a left tail test, the resonable critical region will be (i) C = {0, 1, . . . , 5}
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