Boeing has a contract with an outside company, Opus Enterprise Inc., to supply rivets for the next generation of precision strike aircraft, the F-22 Raptor.  These rivets are used to fasten the wings to the fuselage (body) of the plane, etc.  The contract specifications requires the rivets have an average (µ) diameter of 1.667 cm and a standard deviation of at most 0.23 cm.

A.  How large of a sample must be taken from a shipment of 200,000 rivets, in order to calculate a
     95% confidence interval for the population mean, µ?  The tolerance, allowable error, in the
     diameter measurement is + 0.180 cm.  In a preliminary study, the sample standard deviation
     was 0.492 cm.  Use this value as a point estimate for the population standard deviation, sdsigma.gif (850 bytes),
     in your sample size calculation.

   

B.  Using your answer, n, from Problem A, take the first n numbers (going across, left to right)
     from the following list

1.189 1.364 1.104 1.325 1.502 0.923 2.216 2.309 0.657 0.929
2.142 1.375 1.631 1.949 1.481 1.076 0.743 2.076 1.977 1.416
1.340 1.830 1.466 1.711 2.214 1.736 1.815 1.273 1.661 1.595
1.135 1.399 1.814 1.374 1.340 0.911 1.259 1.198 0.289 1.911
0.813 1.472 1.484 0.346 0.843 1.036 1.793 2.284 1.589 0.983
1.825 1.387 1.632 2.125 1.297 1.113 1.405 1.805 1.975 0.569
1.893 1.557 1.220 1.209 1.646 1.814 1.740 1.307 0.977 1.344
2.003 1.832 1.343 0.591 2.195 2.007 0.966 1.655 1.680 1.268
0.998 2.480 1.938 1.119 1.218 1.662 1.372 0.854 0.858 0.995
1.816 0.836 0.810 1.062 0.863 1.348 2.067 2.418 2.846 1.594

      and calculate a 95% confidence interval for the population mean, µ, the average diameter
      of the rivets.  Use the sample standard deviation, s subx, in the calculation of the
      confidence interval.

1.3605 < µ < 1.7037

      Since 1.667 cm.falls within the interval.  The specification for the mean has been satisfied.

C.  Calculate a 95% confidence interval for the population standard deviation, sdsigma.gif (850 bytes).  Use the
     sample standard deviation, s subx, in the calculation of the confidence interval.

                  

           0.3579 < sdsigma.gif (850 bytes) < 0.60995

     The interval is above 0.23 cm.  The contract specification has not been satisfied.

D.  Based upon the contract's specifications for the rivets, does Boeing accept or reject the
     shipment of 200,000 rivets from Opus Enterprise, Inc.?   Comment on whether the contract
     specifications were satisfied by the confidence intervals. 

     Mr. Milo Bloom,

     Your rivets did satisfy the contract specification for the mean, 1.667 cm falls within the interval, 
     1.3605 < µ < 1.7037      However, your rivets did not satisfy the contract specification for the
     standard deviation.  The specification of 0.23 cm is      below your interval of
     0.3579 < sdsigma.gif (850 bytes) < 0.60995.  Your shipment varies more than the specification.  Regretfully, we
     must reject  your shipment.

     Sincerely,

     J. Sukta

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