Project: Sample Size and Confidence Intervals

Write a report, word processor preferred, presenting a solution to the following problem.  The paper should be no more than one page in length.

Boeing is teamed with Lockheed Martin, Pratt & Whitney and the U.S. Air Force to produce the F-22 Raptor air dominance fighter.  The Raptor's unique combination of stealth, speed, agility, precision and situational awareness make it overwhelmingly effective in its combined air-to-air and air-to-ground mission capability.  This aircraft is the next generation of precision strike aircraft replacing the F-117A.

Boeing has a contract with an outside company, Opus Enterprise Inc., to supply rivets. 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 () diameter of 1.48 cm and a standard deviation of ( )at most 0.23 cm

Your report informs Mr. Milo Bloom, of Opus Enterprise Inc., of the acceptance or rejection of their shipment of 200,000 rivets. Use the following points in the writing of your report. (Show all formulas and calculations used):

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, ?  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.

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, , the average diameter of the rivets.

C.  Calculate a 98% confidence interval for the population standard deviation, Use the sample standard deviation,
     
, in the calculation of the confidence interval.   Click on the Chi-Square symbol, , to go to the Chi-Square table.

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.
 

Click on the hand to view the solution.