Question

Forensic scientists use sensitive equipment to analyze evidence which needs to be calibrated on a regular basis. Suppose 500 forensic scientists each use a certain machine of the same type. Due to a manufactures error, these machines have been installed with a part which has a failure rate of 89% after 600 hours.

Because there are 500 machines, checking all 500 of these machines is costly, therefore a sample of 20 machines is taken and the hours of operation are recorded, The mean usage hours are 850.61 with a standard deviation of 244.67 hours. Estimate the mean usage hours for the 500 machines at 98% confidence and help the forensic scientists determine if these 500 machines need to have the part replaced at alpha level=.01

Answer 1

Solution:-

98% confidence interval for the mean usage hours for the 500 machines is C.I = ( 711.647, 989.573).

C.I = 850.61 + 2.54 × 54.7099

C.I = 850.61 + 138.9631

C.I = ( 711.647, 989.573)

99% confidence interval for the mean usage hours for the 500 machines is C.I = ( 694.085, 1007.135).

C.I = 850.61 + 2.861 × 54.7099

C.I = 850.61 + 156.525

C.I = ( 694.085, 1007.135)

Yes, 500 machines need to have the part replaced at alpha level = 0.01, because 600 is below the lower limit of the confidence interval.