Final answer:
A two-sample t-test is the appropriate statistical method to compare the mean lifespans of A1A Tires to YYZ Tires at the 0.05 significance level. If the p-value of the t-test is less than 0.05, we reject the null hypothesis, indicating evidence supports A1A Tires' claim that their tires last longer.
Step-by-step explanation:
Understanding the Tire Lifespan Hypothesis Test
To decide if A1A Tires' claim that their tires last longer than YYZ Tires is true at the 0.05 level of significance, the appropriate test is a two-sample t-test. Since the claim involves comparing the mean lifespans of two different brands, we do not use a chi-square test, one-sample z-test, or regression analysis as they are not suitable for comparing means between two groups.
Given that the null hypothesis is that there is no difference between the mean lifespans of the two tire brands, and the alternative hypothesis (Ha) is that the mean lifespan of A1A Tires is greater than YYZ Tires, we conduct the t-test and compare its p-value with the alpha level of 0.05. If the p-value is less than 0.05, we reject the null hypothesis, concluding that there is sufficient evidence to support A1A Tires' claim.
As the sample data shows a mean lifespan lower than 50,000 miles, with a p-value lower than 0.05, the decision is to reject the null hypothesis. Therefore, we conclude that, based on the sample data, there is enough evidence to suggest that A1A Tires last longer than YYZ Tires at the 5 percent level of significance.