SOLUTION: A recent newspaper stated that 90% of the world’s large corporations are actively involved in data warehousing. In a random sample of 100 large corporations, what is the probabilit

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Question 819875: A recent newspaper stated that 90% of the world’s large corporations are actively involved in data warehousing. In a random sample of 100 large corporations, what is the probability that at least 85% of them are actively involved in data warehousing?
b) A competitor decided to do a survey of 200 companies and found 168 are so involved. Calculate the 99% confidence interval and write a complete statement.
c) Another newspaper wanted to test the original claim believing that the claim was low. Test the claim at the 0.10 level if a sample of 250 had a result of 92%.
Answer by stanbon(75887) About Me  (Show Source):
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A recent newspaper stated that 90% of the world’s large corporations are actively involved in data warehousing. In a random sample of 100 large corporations, what is the probability that at least 85% of them are actively involved in data warehousing?
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z(0.85) = (0.85-0.90)/sqrt(0.9*0.1/100) = -2.0412
P(p-hat >= 0.85) = P(z >= -2.0412) = 0.9794
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b) A competitor decided to do a survey of 200 companies and found 168 are so involved. Calculate the 99% confidence interval and write a complete statement.
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p-hat = 168/200 = 0.834
ME = 2.5758*sqrt[0.834*0.166/200] = 0.0263
99% CI:: 0.0823-0.0263 < p < 0.0823+0.0263
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c) Another newspaper wanted to test the original claim believing that the claim was low. Test the claim at the 0.10 level if a sample of 250 had a result of 92%.
Ho: p = 0.90
Ha: p > 0.90 (claim)
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p-hat = 0.92
z(0.92) = (0.92-0.90)/sqrt(0.9*0.1/250) = 1.0541
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P-value = P(z > 1.0541) = 0.1459
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Conclusion: Since the p-value is greater than 10% fail to reject Ho.
Conclusiion: The test results do not support the claim.
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Cheers,
Stan H.
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