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

0.3579 <
< 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 <
< 0.60995. Your shipment varies more than the specification. Regretfully, we
must reject
your shipment.
Sincerely,
J. Sukta
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