Question

74. A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles.

Using alpha = 0.05, is the data highly inconsistent with the claim?

In other words, is there convincing evidence (at the 5% significance level) that the deluxe tires actually average less than 50,000 miles before needing to be replaced?

Answer 1

Answer:

Given that:

A particular brand of tires claims that its deluxe tire averages at least 50,000 miles before it needs to be replaced. From past studies of this tire, the standard deviation is known to be 8,000. A survey of owners of that tire design is conducted. From the 28 tires surveyed, the mean lifespan was 46,500 miles with a standard deviation of 9,800 miles.

Test statistic

   (from standard normal table)

Here,

P - value < 0.05 , we reject H₀

There is sufficient evidence to support the claim that the deluxe tires actually average less than

50,000 miles before needing to be replaced .

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