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
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
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