**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. |

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, 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.

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.

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.