Project: 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 (µ) diameter of 1.667 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
     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,

,
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.

C. Calculate a 95% confidence interval for the population standard deviation,

. Use the sample
standard deviation, s subx, in the calculation of the confidence interval.

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.