Homework SourseRefer to the AC sheet The alternating current AC breakdown v
Refer to the AC sheet. The alternating current (AC) breakdown voltage of an insulating liquid indicates its dielectricstrength. The article “Testing Practices for the AC Breakdown Voltage Testing of Insulation Liquids” gave theaccompanying sample observation on breakdown voltage (kV) of a particular circuit under certain conditions.
a. Given ?= 55 and = 5.62, calculate and interpret a 90% Confidence Interval for true average breakdown
voltage . Does it appear that has been precisely estimated?
b. What sample size would be appropriate for the 99% CI to have a width of 2kV (so that is estimated towithin 1 kV with 95% confidence)?
(AC data)
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a)
Note that
Margin of Error E = z(alpha/2) * s / sqrt(n)
Lower Bound = X - z(alpha/2) * s / sqrt(n)
Upper Bound = X + z(alpha/2) * s / sqrt(n)
where
alpha/2 = (1 - confidence level)/2 = 0.05
X = sample mean = 55
z(alpha/2) = critical z for the confidence interval = 1.644853627
s = sample standard deviation = 5.62
n = sample size = 48
Thus,
Margin of Error E = 1.334267641
Lower bound = 53.66573236
Upper bound = 56.33426764
Thus, the confidence interval is
( 53.66573236 , 56.33426764 ) [ANSWER]
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b)
Note that
n = z(alpha/2)^2 s^2 / E^2
where
alpha/2 = (1 - confidence level)/2 = 0.005
Using a table/technology,
z(alpha/2) = 2.575829304
Also,
s = sample standard deviation = 5.62
E = margin of error = width/2 = 2/2 = 1
Thus,
n = 209.5592282
Rounding up,
n = 210 [ANSWER]
