We want to estimate the mean output voltage of a batch of electrical power suppl

Question

We want 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 specifications 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) 95 % , z0.025 =1.96

/sqrt(n) = 3/sqrt(10) =0.9486 ,mean = 110.5

hence confidence interval is (110.5 - 1.96*0.9486 ,110.5 + 1.96*0.9486 ,)

= (108.640,112.359)

specification required - (110± 2.5) =(107.5 ,112.5)

since (108.640,112.359) lies in (107.5,112.5) ,specifications are met.

b)

one-sided 95% confidence bound on the mean output voltage

z0.05 = 1.645 ,

lower limit = 110.5 -1.645 *0.9486 =

108.939

since 108.939 > 107.5 , lower specification limit is met

c) similarly upper limit =

110.5 + 1.645 *0.9486 =112.060   

since 112.06 < 112.5 , upper specification limit is met

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