**Homework 5**

This homework is based on the
following example:

Bearings for high-speed
turbine engines can be made of many different types of compounds. The times to fatigue failure (in units of
millions of cycles) for high-speed bearings were measured for five different
types of compounds. Compounds I and II
are made of an alloy containing lead.
Compounds III, IV, and V are made of an alloy containing iron. Compounds I and III were made by US companies
and compounds II, IV and V were made by foreign companies. The data are listed below:

Compound |
Failure
Time |
Compound |
Failure
Time |
Compound |
Failure
Time |
Compound |
Failure
Time |
Compound |
Failure
Time |

I |
3.03 |
II |
3.19 |
III |
3.46 |
IV |
5.88 |
V |
6.43 |

I |
5.53 |
II |
4.26 |
III |
5.22 |
IV |
6.74 |
V |
9.97 |

I |
5.6 |
II |
4.47 |
III |
5.69 |
IV |
6.9 |
V |
10.39 |

I |
9.3 |
II |
4.53 |
III |
6.54 |
IV |
6.98 |
V |
13.55 |

I |
9.92 |
II |
4.67 |
III |
9.16 |
IV |
7.21 |
V |
14.45 |

I |
12.51 |
II |
4.69 |
III |
9.4 |
IV |
8.14 |
V |
14.72 |

I |
12.95 |
II |
5.78 |
III |
10.19 |
IV |
8.59 |
V |
16.81 |

I |
15.21 |
II |
6.79 |
III |
10.71 |
IV |
9.8 |
V |
18.39 |

I |
16.04 |
II |
9.37 |
III |
12.58 |
IV |
12.28 |
V |
20.84 |

I |
16.84 |
II |
12.75 |
III |
13.41 |
IV |
25.46 |
V |
21.51 |

The goal of this homework is
to compare the average failure times for the bearings made from the 5 different
compounds.

1.
Use PROC MEANS to
calculate the average times to fatigue failure for each of the 5 compounds. Which compound had the longest average time
to fatigue failure? The shortest time?

2.
Use PROC
UNIVARIATE to construct side-by-side box plots.
Based on these plots, do you notice any obvious differences between the
5 compounds?

3.
Use PROC GLM to compute
the analysis of variance for these data.
Based on the overall F-test, is there a significant difference between
the treatment means for the 5 different compounds? State the null and alternative hypotheses for
the test, and report the F-statistic and p-value.

4.
Based on what you
know about the compounds, come up with 2 pre-planned comparisons for the
means. Define the contrasts associated
with these comparisons and use the contrast statement in PROC GLM to test your
hypotheses. Be sure to state the null
and alternative hypotheses for your test, report the p-value, and state your
conclusion in non-statistical terms.

5.
Now, use multiple
comparison methods to compare all possible pairs of treatment means. Using PROC GLM, do the multiple comparisons
using the F-protected LSD, Tukey, and Duncan
methods. For each method, which means
are declared to be the same, and which methods are declared to be significantly
different.

6.
Based on your
findings write a short (one paragraph) summary of your results, and make
recommendations about which compound(s) you would use if your goal was to
create ball-bearings with the longest time to fatigue failure.