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

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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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