You are a quality control engineer and you are asked to analyze the lifetime (in

Question

You are a quality control engineer and you are asked to analyze the lifetime (in hours) of an electronic component mass-produced by a corporation. Management believes that the electronic components are not lasting as long they should. data from your pilot study of 10 randomly selected components resulted in the following lifetimes for parts (in hours): a. Assuming the lifetimes follow a normal distribution, and based on the above sample, develop a 95% confidence interval for the mean lifetime of this type of electronic component. b. The corporation now wants a large analysis. Using the data from your pilot study, you will now determine the sample size needed to ensure a confidence of 99% and an error of at most 2 hours. How large is your sample? c. Based on the sample size you just came up with, you then took a sample. After several days of collecting data, you found a sample average of 50 hours with a standard deviation of 8.1 hours. Calculate a 95% confidence interval for the true population mean of the lifetime of these electronic parts.

Explanation / Answer

a)

for 95% CI and (n-1=9) degree of freedom ; t=2.262

hence confidence interval =sample mean -/+ t*std error =42.2556 ; 55.7444

b)

here std deviation s=9.428

for 99% CI, z=2.5758

and margin of error E =2

hence sample size n=(z*s/E)2 =~148

c) for 147 degree of freedom and 95% CI, t=1.976

std error =std deviaiton/(n)1/2 =0.6658

hence confidence intercal =50 -/+ t*std error =48.6842 ; 51.3158

X 50 48 61 34 42 63 57 51 39 45 mean(X) 49.000 std deviation(S) 9.428 std error =S/(n)1/2 2.981

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