Tires are among the most commonly replaced parts on vehicles. They are not cheap and shopping for them is confusing. When we look for tires, many of us pay attention to the warranty that accompanies them as a way of getting reliable and long-lasting tires - sometimes paying a hefty premium for high performance. Tire manufacturers test their tires in house. Tires are inflated to the optimal pressure and then the tires spin on specially designed treadmills. The thread-life warranties are presented in a mileage estimate. If a tire has worn out evenly across the tread well before its estimated mileage limit, it may qualify for replacement. Of course, the tire manufacturer would like to minimize warranty replacements by making sure that their tires meet the mileage standard. To this end, the production manager of a tire company is testing their mileage warranty of 30,000 miles. To do the test, 60 tires are put through the treadmill test. When the tires are worn down to the 2/32nd thread-wear indicators, the mileage is recorded. You have the result of one such sample in the file What is the required sample size, if the management wants to be within 250 miles of the actual population mean? Assumptions being that: The lower bound of the 95% confidence interval of the mean mileage for the tires is 29489.95 The upper bound of the 95% confidence interval of the mean mileage for the tires is 30781.59 The probability of finding a sample with a mean of fewer than 30,000 miles is 0.337

MATLAB: An Introduction with Applications
6th Edition
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Tires are among the most commonly replaced parts on vehicles. They are not cheap and shopping for them is confusing. When we look for tires, many of us pay attention to the warranty that accompanies them as a way of getting reliable and long-lasting tires - sometimes paying a hefty premium for high performance.

Tire manufacturers test their tires in house. Tires are inflated to the optimal pressure and then the tires spin on specially designed treadmills.

The thread-life warranties are presented in a mileage estimate. If a tire has worn out evenly across the tread well before its estimated mileage limit, it may qualify for replacement.

Of course, the tire manufacturer would like to minimize warranty replacements by making sure that their tires meet the mileage standard. To this end, the production manager of a tire company is testing their mileage warranty of 30,000 miles. To do the test, 60 tires are put through the treadmill test. When the tires are worn down to the 2/32nd thread-wear indicators, the mileage is recorded. You have the result of one such sample in the file

What is the required sample size, if the management wants to be within 250 miles of the actual population mean?

Assumptions being that:

The lower bound of the 95% confidence interval of the mean mileage for the tires is 29489.95

The upper bound of the 95% confidence interval of the mean mileage for the tires is 30781.59

The probability of finding a sample with a mean of fewer than 30,000 miles is 0.337

 

Tire #
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
Mileage
31564
27886
28822
27326
31535
31880
28376
29664
25001
34981
32048
27672
31267
31512
35228
25089
32372
29749
28670
34683
34551
32811
30535
26741
30874
27535
28444
27504
30179
31491
28531
29715
30103
33841
28462
27535
34548
27165
28906
32027
31802
31878
31972
30650
31514
27820
34669
30534
30598
29459
28559
28630
33827
26831
28394
27616
29207
30024
29883
27456
Transcribed Image Text:Tire # 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Mileage 31564 27886 28822 27326 31535 31880 28376 29664 25001 34981 32048 27672 31267 31512 35228 25089 32372 29749 28670 34683 34551 32811 30535 26741 30874 27535 28444 27504 30179 31491 28531 29715 30103 33841 28462 27535 34548 27165 28906 32027 31802 31878 31972 30650 31514 27820 34669 30534 30598 29459 28559 28630 33827 26831 28394 27616 29207 30024 29883 27456
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