to estimate the mean output voltage of a batch of electrical power supply units
ID: 3043220 • Letter: T
Question
to estimate the mean output voltage of a batch of electrical power supply units A random sample of 10 units is tested, and the sample mean is calculated to be 110.5 volts Assume that the measurements are normally distributed with = 3 volts. (a) Calculate a two-sided 95% CI on the mean output voltage. Suppose that the spec- ifications on the true mean output voltage are 110 ± 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
a)
One-Sample Z
The assumed standard deviation = 3
N Mean SE Mean 95% CI
10 110.500 0.949 (108.641, 112.359)
specification on true mean output = (107.5 , 112.5)
since
(108.641, 112.359) lies completely inside (107.5 , 112.5)
specifications are met
b)
95 % lower confidence bound
One-Sample Z
The assumed standard deviation = 3
N Mean SE Mean 95% Lower Bound
10 110.500 0.949 108.940
108.940 > 107.5 , hence specifications are met
c)
One-Sample Z
The assumed standard deviation = 3
N Mean SE Mean 95% Upper Bound
10 110.500 0.949 112.060
sicne 112.06 < 112.5
specifications are met
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