On a certain day, a large number of fuses were manufactured, each rated at 15 A. A sample of 75 fuses is drawn from the day’s production, and 17 of them were found to have burnout amperages greater than 15 A. Find a 95\% confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15 A.

abondantQ

abondantQ

Answered question

2021-08-04

On a certain day, a large number of fuses were manufactured, each rated at 15 A. A sample of 75 fuses is drawn from the day’s production, and 17 of them were found to have burnout amperages greater than 15 A.
a) Find a 95% confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15 A.
b) Find a 98% confidence interval for the proportion of fuses manufactured that day whose burnout amperage is greater than 15 A.
c) Find the sample size needed for a 95% confidence interval to specify the proportion to within ±0.05.

Answer & Explanation

Ian Adams

Ian Adams

Skilled2021-08-17Added 163 answers

a) Given x=17 and n=75
p^=xn=1775=0.2267
The critical value corresponding with 95% confidence level is 1.96
95%CI=p^± zcriticalp^(1p^)n
=0.2267±1.960.2267(10.2267)75
=(0.1319, 0.3215)
b) The critical value corresponding with 98% confidence level is 2.33
95%CI=p^± zcriticalp^(1p^)n
=0.2267±2.330.2267(10.2267)75
=(0.1141, 0.3393)
c) The critical value corresponding with 95% confidence level is 1.96
ME=0.05
sample size =(zcriticalME)2p(1p)
=(1.960.05)20.5(10.5) Let p=0.5
=348.16
384

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