Question

3.       A treadmill manufacturer has developed a new machine with softer tread and better fans than its current model. The manufacturer believes these new features will enable runners to run for longer times than they can on its current machines. To determine whether the desired result is achieved, the manufacturer randomly sampled 35 runners. Each runner was measured for one week on the current machine and for one week on the new machine. The weekly total number of minutes for each runner on the two types of machines was collected. The results are contained in the file . At the 0.02 level of significance, can the treadmill manufacturer conclude that the new machine has the desired result? Treadmill.xlsx

a.       Specify the population parameter(s) of interest (proportion or mean):

b.       Formulate the null (H0) and alternate (HA) hypotheses:

c.       Specify the level of significance (alpha, a, probability of a Type I error):

d.       What is/are the critical value(s)?

e.       What is/are the value(s) of the test statistic?

f.        Based on your graph, do you reject H0 or do not reject H0? Explain

g.       To validate your results, we’ll also check our p-value. What is the p-value?

h.       Based on your p-value, do you reject H0 or do not reject H0? Explain

i.         State your summary statement of the conclusion in non-technical terms.

Runner	Current	New
1	302	404
2	289	494
3	380	251
4	438	343
5	342	402
6	447	362
7	330	363
8	286	533
9	252	187
10	421	397
11	307	387
12	444	251
13	369	244
14	336	208
15	206	276
16	450	430
17	252	402
18	280	406
19	473	548
20	432	531
21	239	389
22	350	293
23	185	256
24	371	513
25	233	308
26	536	217
27	238	499
28	306	284
29	187	257
30	484	501
31	431	449
32	524	442
33	412	411
34	460	451
35	287	371

Answer 1

Solution:-

Given that

A treadmill manufacturer has developed a new machine with softer tread and better fans than its current model. The manufacturer believes these new features will enable runners to run for longer times than they can on its current machines. To determine whether the desired result is achieved, the manufacturer randomly sampled 35 runners. Each runner was measured for one week on the current machine and for one week on the new machine. The weekly total number of minutes for each runner on the two types of machines was collected. The results are contained in the file . At the 0.02 level of significance, can the treadmill manufacturer conclude that the new machine has the desired result

a. Specify the population parameter(s) of interest (proportion or mean):

Population parameter mean

b. Formulate the null (H0) and alternate (HA) hypotheses:

v/s  

where

= mean of new tread mill

= mean of old tread mill

c. Specify the level of significance (alpha, a, probability of a Type I error):

d. What is/are the critical value(s)?

The teststatistic model is,

Here

e. What is/are the value(s) of the test statistic?

Here

f. Based on your graph, do you reject H0 or do not reject H0? Explain

Accept at 2% loss

g.To validate your results, we’ll also check our p-value. What is the p-value?

p - value

= p(t > 0.9279)

= 0.1783

h. Based on your p-value, do you reject H0 or do not reject H0? Explain

p -value = 0.17 > 0.02

Accept at 2% loss

i. State your summary statement of the conclusion in non-technical terms.

Average mean of new tread mill and current tread mill are equal.

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