Question 1088405: 8) A manufacturer considers his production process to be out of control when defects exceed 8) 3%. In a random sample of 85 items, the defect rate is 5.9% but the manager claims that this
is only a sample fluctuation and production is not really out of control. At the 0.01 level of significance, test the manager's claim.
9) A poll of 1,068 adult Americans reveals that 48% of the voters surveyed prefer the 9) Democratic candidate for the presidency. At the 0.05 level of significance, test the claim
that at least half of all voters prefer the Democrat.
Please explain how to set these problems up. Thank you!
Answer by Boreal(15235)   (Show Source):
You can put this solution on YOUR website! 85*0.059=5 defects
Use binomial
probability 5 or more defects in 85 given that the rate is 3%: That is nCx (probability of failure^x)(probability of success^(n-x))
85C5(.03^5)(.97^80)=0.0697 for 5
there will be non=zero values for 6, 7,, 8...
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use 1 sample proportion with np at the borderline of acceptable (np=3)
Critical value is z>2,33 for 1 way test.
z=(.059-0.03)/sqrt (p*(1-p))/n
sqrt term is .03*.97/85=0.0185
z=0.029/0.0185=1.56
Not significant at the 0.01 level.
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For the second one, can do a confidence interval as well as a z-test
Will do the z-test
one sample proportion same as last part
critical value z>1,645 for a 1-way test
z=(0.50-0.48)/sqrt (0.5*0.5/1068)
=0.02/0.0153=1.31
Cannot exclude 50% as a plausible percentage based on these data.
quick check: 1/sqrt (sample size) is approximate error for 2 sided test, and that is +/-0.03, so that 50% is plausible.
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