Question

The authors of a research article compared two different instruments for measuring a person's capacity to breathe 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 the 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 samples from their respective populations of measurement. Data values from this paper are given in the accompanying table.

Subject	Mini Wright Meter	Wright Meter
1	511	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	443	433
11	432	417
12	626	656
13	260	267
14	477	478
15	259	178
16	350	423
17	451	425

Use the given data to determine if there is convincing evidence that the mean reading differs for the two instruments. (Hint: See Example 13.2.) (Use

α = 0.05.

Use

μ_d = μ_mini-Wright − μ_Wright.)

State the appropriate null and alternative hypotheses.

H₀: μ_d = 0

H_a: μ_d < 0

H₀: μ_d = 0

H_a: μ_d ≠ 0

     

H₀: μ_d = 0

H_a: μ_d > 0

H₀: μ_d ≠ 0

H_a: μ_d = 0

H₀: μ_d < 0

H_a: μ_d = 0

Find the test statistic and P-value. (Use a table or technology. Round your test statistic to one decimal place and your P-value to three decimal places.)

t=

P-value =

State the conclusion in the problem context.

We reject H₀. We have convincing evidence that the mean reading differs for the two instruments.

We fail to reject H₀. We do not have convincing evidence that the mean reading differs for the two instruments.     

We reject H₀. We do not have convincing evidence that the mean reading differs for the two instruments.

We fail to reject H₀. We have convincing evidence that the mean reading differs for the two instruments.

Answer 1

x: Mini Wright Meter

y: Wright Meter

Subject	x	y	d=x-y	d-d̅	(d-d̅)^2
1	511	494	17	14.94	223.2388
2	430	395	35	32.94	1085.121
3	520	516	4	1.94	3.768166
4	428	434	-6	-8.06	64.94464
5	500	476	24	21.94	481.4152
6	600	557	43	40.94	1676.18
7	364	413	-49	-51.06	2607.003
8	380	442	-62	-64.06	4103.533
9	658	650	8	5.94	35.29758
10	443	433	10	7.94	63.06228
11	432	417	15	12.94	167.474
12	626	656	-30	-32.06	1027.768
13	260	267	-7	-9.06	82.06228
14	477	478	-1	-3.06	9.356401
15	259	178	81	78.94	6231.709
16	350	423	-73	-75.06	5633.827
17	451	425	26	23.94	573.1799
		Total	35		24068.94
		mean=d̅	Total/17
		d̅=	2.06