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.
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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 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,
.
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,
,
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
.
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 <
< 0.56335.
Your shipment varies more than the specification.
Regretfully, we must reject
your shipment.
Sincerely,
J. Sukta
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