Test the indicated claim about the means of two populations. Assume that the two samples are independent simple random samples selected from normally distributed populations. Do not assume that the population standard deviations are equal. Two types of flares are tested and their burning times (in minutes) are recorded. The summary statistics are given below.

underbar(Brand X)​ underbar(Brand Y)
n = 35 n = 40
overbar(x) = 19.4 min overbar(x) = 15.1 min
s = 1.4 min s = 0.8 min

Use a 0.05 significance level to test the claim that the two samples are from populations with the same mean. Use the traditional method of hypothesis testing.