To provide “extra distance” to golf balls, a golf equipment manufacturer has developed a new batch of golf balls. When testing the driving distance using a mechanical driving device, the manufacturer sampled 100 new developed golf balls, which give an average distance of 285 yards and a standard deviation of 15 yards. He compared his result with one of his competitor’s production of 180 golf balls with a mean distance of 258 yards and a standard deviation of 20 yards.

a. At a 1% of significance level, conduct a hypothesis testing to determine whether the new golf balls can achieve 15 yards more than the competitor.

b. What assumptions should be made to run the hypothesis testing in part a?