Final answer:
The question involves normal distribution and hypothesis testing in statistics, where a sample mean and standard deviation are used to test claims about a population mean based on the normal distribution model.
Step-by-step explanation:
The subject matter pertains to normal distribution and hypothesis testing in statistics, which is a branch of mathematics. When examining the lifespan of tires, we use the sample mean, sample standard deviation, and the known or assumed population standard deviation to form a hypothesis about the population mean. For instance, if a tire company claims that their tires last at least 50,000 miles on average, we could use a hypothesis test to determine whether this claim holds true based on the data gathered from sample observations. When the p-value calculated from the test statistic (such as a Z-score) is less than the chosen significance level (alpha), we reject the null hypothesis. In this case, it would suggest that the evidence supports the alternative hypothesis that the tires have a lower average lifespan than claimed.
In practice, if a sample of 28 tires has a mean lifespan of 46,500 miles with a standard deviation of 9,800 miles, and we're using an alpha of 0.05, then a low p-value such as 0.0103 would lead us to reject the null hypothesis, concluding that the average lifespan is indeed less than 50,000 miles.