The manufacturer of a particular brand of tires claims they average at least 50,000 miles before needing to be replaced. From past studies of this tire, it is known that the population standard deviation is 8,000 miles.

A survey of tire owners was conducted. From the 21 tires surveyed, the mean lifespan was 40500 miles. Using alpha = 0.05, can we prove that the data in inconsistent with the manufacturers claim?

We should use a ? z t test.

What are the correct hypotheses? 

H₀: Select an answer s² x̄ σ σ² s p μ p̂ ? ≠ < ≤ ≥ = >

H_a: Select an answer s μ p̂ s² σ σ² x̂ p ? ≤ ≠ > ≥ < =

Based on the hypotheses, find the following:

Test Statistic=

p-value=

The correct decision is to Select an answer Fail to reject the null hypothesis Accept the null hypothesis Accept the alternative hypotheis Reject the null hypothesis .

The correct conclusion would be: Select an answer There is enough evidence to conclude that the tires last fewer miles than claimed There is not enough evidence to conclude that the tires last fewer miles than claimed There is enough evidence to conclude that the tires do not last fewer miles than claimed There is not enough evidence to conclude that the tires do not last fewer miles than claimed .