Question

02) The alternating current (AC) breakdown voltage of an insulating liquid indicates its dielectric strength. The article "Testing Practices for the AC Breakdown Voltage Testing of Insulation Liquids" (IEEE Electrical Insulation Magazine, 1995: 21- 26) gave the accompanying sample observations on breakdown voltage (kV) of a particular circuit under certain conditions. 62 50 53 57 41 53 55 61 59 64 50 53 64 62 50 68 54 55 57 50 55 50 56 55 46 55 53 54 52 47 47 55 57 48 63 57 57 55 53 59 53 52 50 55 60 50 56 58 i) ii) Calculate and interpret a 95% CI for true average breakdown in the population Calculate the 95% upper bound for true average breakdown.

Answer 1

1)

95% Confidence interval

C.I=

X+1.960/ yn

=54.708+1.96*5.231/sqrt(48) &=54.708-1.96*5.231/sqrt(48)

= 95% Confidence Interval: 54.708 ± 1.48
(53.2 to 56.2)

"With 95% confidence, the population mean is between 53.2 and 56.2, based on 48 samples."

Short Styles:
54.708 (95% CI 53.2 to 56.2)
54.708, 95% CI [53.2, 56.2]

Margin of Error: 1.48
(to more digits: 1.48)

Sample Size: 48
Sample Mean: 54.708
Standard Deviation: 5.231
Confidence Level: 95%

2)

95% upper bound= mean+margin of error

=54.708+1.48

=56.19

95% upper bound=56.19