A manufacturing company is looking to reduce the amount of time it takes to assemble one of their key products. Previously, the average assembly time was 55 minutes with a standard deviation of 10 minutes. A random sample of 40 products was recently assembled. The individual assembly times in minutes were:
62, 47, 51, 59, 46, 58, 54, 49, 52, 50
60, 53, 48, 43, 61, 57, 44, 55, 41, 56
59, 51, 42, 45, 63, 47, 52, 54, 51, 57
49, 51, 42, 59, 45, 61, 56, 53, 55, 62
Conduct a hypothesis test at the 5% significance level to determine if the mean assembly time has changed from the previous value of 55 minutes. What assumption about the population distribution is required to conduct this test?