Question

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 values - sometimes paying a hefty premium for high performance.

Tire manufacturers test their tires in house. Tires are inflated to the optimal psi and then the tires spin on specially designed treadmills. The thread-life warranties are presented in 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 this 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, 50 tires are put through the treadmill test. When the tires are worn down to the 2/32^nd thread-wear indicators, the mileage is recorded. You have the result of one such sample in the file Tire_Mileage.xlsx.

Based on the sample, what is the lower bound of the 95% confidence interval of the mean mileage for the tires?

NOTE: Enter numerical values with no commas and with 2 decimal places.

Tire #	Mileage
1	30564
2	28886
3	29822
4	29326
5	31535
6	31880
7	28376
8	29664
9	25001
10	31981
11	31048
12	29672
13	33267
14	31512
15	35228
16	27089
17	31372
18	32749
19	28670
20	31683
21	34551
22	31811
23	29535
24	25741
25	28874
26	28535
27	28444
28	27504
29	32179
30	31491
31	29531
32	29715
33	30103
34	33841
35	28462
36	29535
37	34548
38	28165
39	30817
40	34027
41	31802
42	31878
43	31972
44	30650
45	31514
46	28820
47	32669
48	33534
49	30598
50	29459

Answer 1

From the given data, the following statistics are calculated:

n = 50

= 30592.6

s = 2217.9787

= 0.05

df = 50 - 1 = 49

From Table, critical values of t = 0.063

the lower bound of the 95% confidence interval of the mean mileage for the tires is given by:

So,

Answer is:

30572.83