Question 359895: An engineering firm is evaluating their back charges. They originally believed their average back charge was $1800. They are concerned that the true average is higher, which could hurt their quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample mean back charge to be $1950. If the standard deviation of back charges is $500, and alpha = 0.05, should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! An engineering firm is evaluating their back charges. They originally believed their average back charge was $1800. They are concerned that the true average is higher, which could hurt their quarterly earnings. They randomly select 40 customers, and calculate the corresponding sample mean back charge to be $1950. If the standard deviation of back charges is $500, and alpha = 0.05, should the engineering firm be concerned? Perform an appropriate hypothesis test, showing the necessary calculations and/or explaining the process used to obtain the results
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Ho: u = 1800
Ha: u > 1800
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t(1950) = (1950-1800)/[500/sqrt(40)] = 1.8974
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p-value: P(t > 1.8974 when df = 39) = tcdf(1.8974,100,39) = 0.0326
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Conclusion: Since the p-value is less than 5%, reject Ho.
The test results do not support the claim that u = 1800.
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Cheers,
Stan H.
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