Each day, more than 10,000 customers shop at a business. A sample with a size of n = 100 from location A has an average customer stay of 45 min. The actual duration has a normal distribution with an unknown arithmetic mean μ and a variance of S² = 152 min². According to management, the mean stay is 55 min. Test whether a sample can rebut this claim with a probability of error of α ¼ 0.05. Explain your answer.