SOLUTION: A lab for manager claims that faulty readings on piece equipment are generated about 10% of the time ,but a researcher believes it to be higher.a random sample of 400 records cont

Question 1083822: A lab for manager claims that faulty readings on piece equipment are generated about 10% of the time ,but a researcher believes it to be higher.a random sample of 400 records contains 60 error -what is evidence do you have at the 0.05 level significance to support the lab manager is statement or otherwise? -A further random sample of the same size ,45 errors .what would your conclusion have been on basis of this sample
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
A lab for manager claims that faulty readings on piece equipment are generated about 10% of the time ,but a researcher believes it to be higher.a random sample of 400 records contains 60 error -what is evidence do you have at the 0.05 level significance to support the lab manager is statement or otherwise? -
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Ho: p <= 0.10
Ha: p > 0.10 (claim)
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p-hat = 60/400 = 6/40 = 0.15
z(0.15) = (0.15-0.10)/sqrt(0.15*0.85/400) = 2.8
Using P-value criteria.
P-value = P(z > 2.8) = normalcdf(2.8,100) = 0.003
Conclusion:: Since the P-value is less than 5%, reject Ho.
Test results support the claim.
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A further random sample of the same size 45 errors .what would your conclusion have been on basis of this sample
p-hat = 45/400 = 0.11
z(0.11) = (0.11-0.10)/sqrt(0.11*0.89/400) = 0.64
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P-value = P(z > 0.64) = normalcdf(0.64,100) = 0.26
Conclusion:: Sine the P-value is greater than 5%, fail to reject Ho.
Test results do no support the claim.
Cheers,
Stan H.
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Cheers,
Stan H.
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