The authors of a paper compared two different instruments for measuring a person's capacity for breathing out air. (This measurement is helpful in diagnosing various lung disorders.) The two instruments considered were a Wright peak flow meter and a mini-Wright peak flow meter. Seventeen people participated in the study, and for each person air flow was measured once using the Wright meter and once using the mini-Wright meter.

The Wright meter is thought to provide a better measure of air flow, but the mini-Wright meter is easier to transport and to use. Use of the mini-Wright meter could be recommended as long as there is not convincing evidence that the mean reading for the mini-Wright meter is different from the mean reading for Wright meter. For purposes of this exercise, you can assume that it is reasonable to consider the 17 people who participated in this study as representative of the population of interest. Data values from this paper are given in the accompanying table.

Subject Mini Wright Wright
Meter Meter
1 516 494
2 430 395
3 520 516
4 428 434
5 500 476
6 600 557
7 364 413
8 380 442
9 658 650
10 444 433
11 432 417
12 626 656
13 260 267
14 477 478
15 259 178
16 350 423
17 451 421

Use the given data to determine if there is convincing evidence that the mean reading differs for the two instruments. (Use a statistical computer package to calculate the P-value. Use μmini-Wright − μWright. Round your test statistic to two decimal places, your df down to the nearest whole number, and your P-value to three decimal places.)