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 1.48 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 98% confidence  
      interval for the population mean, µ?  The tolerance, allowable error, in the diameter measurement is + 0.150 cm.
      The formula for sample size requires the population standard deviation, sdsigma.gif (850 bytes).  However, the population standard 
      deviation is unknown.  To estimate the population s.d. take a pilot sample of size 10 (use the first 10 numbers going   
       across, left to right).  The sample standard deviation, , of these 10 rivets will be used as an estimate 
       for the population  standard deviation.  Round the sample standard deviation to four decimal places.  
       Use this value as a point estimate  for the population standard deviation, sdsigma.gif (850 bytes), in your sample size calculation.  
       When calculating the sample size, round the z score to  2 decimal  places.

      = 0.5395250586 0.5395   This is the estimate for sdsigma.gif (850 bytes).

      invnorm(0.99, 0, 1) = 2.326347877 2.33

      

B.  Using your answer, n, from Problem A, take the first n numbers (going across, left to right) from the following list.
      You already have ten numbers, continue with 2.142 as the 11th number.

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

      Calculate a 98% confidence interval for the population mean, µ, the average diameter of the rivets.

Using T-Interval:  1.3245 <  < 1.5809

1.48 falls within the interval.  The rivets pass the first specification.

C.  Calculate a 98% confidence interval for the population standard deviation, .  Use the sample standard deviation,
     , rounded to 4 places, in the calculation of the confidence interval.  See the Chi-Square Table accompanying this
     project.

      = 0.4538529212 0.4539

The entire interval is above the specification of 0.23.  The rivets fail the second specification.

 

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, 1.48 cm falls within the interval, 
        1.3245 <  < 1.5809.  However, your rivets did not satisfy the contract specification for the
      standard deviation.  The specification of 0.23 cm is below your interval of 0.37896 < sdsigma.gif (850 bytes) < 0.56335. 
      Your shipment varies more than the specification.   Regretfully, we must reject  your shipment.

      Sincerely,

        J. Sukta

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