Final answer:
To assess the validity of a tire's advertised lifespan using statistical hypothesis testing, one compares the sample mean against the claimed population mean. If the calculated p-value is below the alpha level of 0.05, one would reject the null hypothesis and consider the evidence sufficient to dispute the claim. Since specific p-value and t-statistic are not provided, a conclusive decision cannot be reached.
Step-by-step explanation:
The tire manufacturer's claim that their deluxe tire averages at least 50,000 miles before needing replacement can be tested using a statistical hypothesis test, specifically a one-sample t-test because we compare a sample mean to a population mean with a known standard deviation. To test such a claim at an alpha level of 0.05, we must state our null hypothesis (H0) as the tire life being equal to or greater than 50,000 miles, and our alternative hypothesis (Ha) as the tire life being less than 50,000 miles.
From the data provided, the sample mean tire life is 46,500 miles with a sample standard deviation of 9,800 miles from a sample size of 28 tires. The known population standard deviation is not taken into account because the sample standard deviation is used for calculation in this instance. Using these figures, we calculate a t-statistic and compare it to a t-distribution with 27 degrees of freedom to find the p-value.
If the calculated p-value is less than 0.05, we reject the null hypothesis and conclude that there is enough evidence to support the claim that the average tire life is less than 50,000 miles. In this scenario, given the provided summary statistics, there would be sufficient statistical evidence to reject the null hypothesis at the 0.05 alpha level, suggesting that the claim of the average life of tires being at least 50,000 miles is likely false. However, the exact p-value and t-statistic are not provided and therefore an exact conclusion cannot be made from the information given.