We want to estimate the mean output voltage of a batch of electrical power suppl
ID: 3217418 • Letter: W
Question
We want to estimate the mean output voltage of a batch of electrical power supply units. A random sample of 1 units is tested, and the sample mean is calculated to be 110.5 volts. Assume that the measurements are normally distributed with sigma = 3 volts. a) Calculate a two- sided 95% CI on the mean output voltage. Suppose that the specifications on the true mean output voltage are 110 plusminus 2.5 volts. Explain how the CI can be used to check whether these specifications are met. b) Suppose that only the lower specification is applicable, since the main concern is that too low a voltage may cause malfunction of the equipment. Calculate an appropriate one-sided 95% confidence bound on the mean output voltage and explain how it can be used to check whether the lower specification limit is met. c) Suppose that only the upper specification is applicable, since the main concern is that too high a voltage may cause malfunction of the equipment. Calculate an appropriate one-sided 95% confidence bound on the mean output voltage and explain how it can be used to check whether the upper specification limit is met.Explanation / Answer
One-Sample Z
The assumed standard deviation = 3
N Mean SE Mean 95% CI
100 110.500 0.300 (109.912, 111.088)
True Mean can lie between 107.5 to 112.5
Since the 95% CI for sample mean lies within the tolerance limit , we can conclude that the specifications are met.
b)
One-Sample Z
The assumed standard deviation = 3
95% Lower
N Mean SE Mean Bound
100 110.500 0.300 110.007
Since the lower bound of 95% CI for sample is 110.007 which is greater than 107.5 we can conclude that the lower specification is met.
c)
One-Sample Z
The assumed standard deviation = 3
95% Upper
N Mean SE Mean Bound
100 110.500 0.300 110.993
Since 95% upper bound is 110.993 and it is within the 112.5 we can conclude that the specification are met.
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