Final answer:
The subject question is related to performing a hypothesis test in statistics to verify a manufacturer's claim about the product mean life, using an alpha of 0.05 and p-value criteria.
Step-by-step explanation:
The question involves performing a hypothesis test to verify a manufacturer's claim about the mean life of its products. When conducting a hypothesis test, we assume a null hypothesis (usually the claim we are testing) and an alternative hypothesis that we are trying to find evidence for. In this scenario, the null hypothesis would be 'the mean life of the product is x years' and the alternative hypothesis would be 'the mean life of the product is more than x years'.
With a given alpha level of 0.05, we look at the p-value which represents the probability of obtaining test results at least as extreme as the results actually observed, under the assumption that the null hypothesis is correct. If this p-value is less than the alpha level, we reject the null hypothesis. In this case, the decision to reject is based on the p-value is less than 0.05, indicating that there is sufficient statistical evidence to conclude that the actual mean life of the product is more than x years.
In performing such tests, we would typically use the z-distribution or t-distribution depending on the availability of the population standard deviation and the sample size. Tools such as a calculator or software would be used to calculate the p-value.