Final answer:
Using hypothesis testing with an alpha of 0.05 and the provided data, the Z-score of -2.315 and p-value of 0.0103 suggest that the sample mean of 46,500 is highly inconsistent with the claimed average lifespan of at least 50,000 miles for the tires.
Step-by-step explanation:
To determine if the data is highly inconsistent with the claim that a particular brand of tires averages at least 50,000 miles before needing replacement, a hypothesis test can be conducted. Here, Ha: <50,000 represents the alternative hypothesis which suggests that the average lifespan of the tire is less than 50,000 miles. To test this claim, we consider X as the average lifespan of a brand of tires. Given that the sample size is relatively small (28 tires), but we know the population standard deviation, we assume a normal distribution for the sake of the hypothesis test.
The provided survey data shows a sample mean of 46,500 miles and a sample standard deviation of 9,800 miles. With an alpha level of 0.05, a Z-score of Z = -2.315 is computed, which corresponds to a p-value of 0.0103. The small p-value indicates that the observed sample mean of 46,500 miles is highly inconsistent with the claim since the p-value is less than the alpha level of 0.05. Therefore, we would reject the null hypothesis and accept the alternative hypothesis that the tires do not last 50,000 miles on average.