The data sheet labeled rebound comes from a company which supplies a major automobile manufacturer with shock absorbers. A major quality characteristic of interest is the “force transferred through the shock absorber when the shank is forced out of the cylinder”. The exact technical definition of this test is not important for us. What we do need to understand is that the manufacturer only considers the shock to be an acceptable part if the force measurement is between 485 and 585. The shock manufacturer and the auto manufacturer are arguing over the following issue. Before the shock
The data sheet labeled rebound comes from a company which supplies a major automobile manufacturer with shock absorbers. A major quality characteristic of interest is the “force transferred through the shock absorber when the shank is forced out of the cylinder”. The exact technical definition of this test is not important for us. What we do need to understand is that the manufacturer only considers the shock to be an acceptable part if the force measurement is between 485 and 585.
The shock manufacturer and the auto manufacturer are arguing over the following issue. Before the shock is finally shipped, it is filled with gas. After it is filled with gas it becomes very difficult to measure the force quantity we are interested in. The shock makers would like to make the
measurement before the shock is filled with gas. The auto maker is concerned that there may be a difference in the force before and after the shock is filled with gas and so would like to make the measurement after it is filled. The shock maker claims that there is little difference between the before and after measurements so that the before measurement can be used. To investigate this we have both the before (column1) and after (column2) measurement on 35 shocks.
a) Plot the after measurement vs the before measurement. Does this look like the kind of data that linear regression can describe? Why does it make sense to choose the after measurement as our Y and the before as our X in this example?
b) Obtain 95% confidence intervals for the slope and intercept.
c) From the shock makers point of view what hypotheses would be of interest to test for the slope. That is, what would the shock maker most like the true slope to be? Test whether the slope is equal to the proposed value.
d) Suppose the before measurement of a shock is 550. What is the expected value for the after measurement?
| reboundb | rebounda |
| 528 | 528 |
| 507 | 497 |
| 535 | 523 |
| 532 | 511 |
| 541 | 523 |
| 533 | 525 |
| 503 | 506 |
| 565 | 553 |
| 557 | 539 |
| 534 | 519 |
| 566 | 567 |
| 524 | 507 |
| 616 | 595 |
| 537 | 523 |
| 515 | 509 |
| 610 | 596 |
| 525 | 524 |
| 512 | 502 |
| 528 | 518 |
| 568 | 564 |
| 551 | 548 |
| 559 | 561 |
| 527 | 517 |
| 560 | 553 |
| 536 | 520 |
| 590 | 588 |
| 610 | 598 |
| 557 | 544 |
| 511 | 519 |
| 533 | 533 |
| 519 | 494 |
| 514 | 511 |
| 573 | 561 |
| 510 | 500 |
| 569 | 555 |
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