1) some company claims that the defective rate for their product is most 3%. to

Question

1) some company claims that the defective rate for their product is most 3%. to test the claim, we check 100 of the product. we set the decision making rule as: If we find the number of defective is at most 4, we will accept the claim. Otherwise, we will reject the claim. Based of this rule, find the probability for the making Type 1 error.

2) Consider the following test of hypothesis: H0 : =50 , H1: =56 Assume =10 and sample size n=64. Suppose the testing rule is: If x < 52, we accept H0, otherwise, we reject H0. For this testing, find , that is, the probability for making Type II error

Explanation / Answer

Solution 1:

Solution:

Sample proportion, p’ = 4/100 = 0.04

Z = (p’ – p)/p (1 – p)

Z = (0.04 – 0.03)/0.03*0.97/100

Z = 0.59

Using Z-tables, the probability is

P [Z > 0.59] = 1 – 0.7224 = 0.2778

Hence, the probability for making Type 1 error is 0.2778.

Solution 2:

Solution:

Z = (X-bar - µ)/ (/n)

Z = (52 – 50)/ (10/64)

Z = 1.6

Using Z-tables, the probability is

P [Z < 1.6] = 0.9452

Hence, the probability of making type ii error is 0.9452.

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