The article “Effects of Aerosol Species on Atmospheric Visibility in Kaohsiung City, Taiwan” (C. Lee, C. Yuan, and J. Chang, Journal of Air and Waste Management, 2005:1031–1041) reported that for a sample of 20 days in the winter, the mass ratio of fine to coarse particles averaged 0.51 with a standard deviation of 0.09, and for a sample of 14 days in the spring the mass ratio averaged 0.62 with a standard deviation of 0.09. Let μ₁ represent the mean mass ratio during the winter and let μ2 represent the mean mass ratio during the summer. It is desired to test H₀ :μ₂ − μ₁ = 0 versus H₁ :μ₂ − μ₁ = 0.

a. Someone suggests that since the sample standard deviations are equal, the pooled variance should be used. Do you agree? Explain.

b. Using an appropriate method, perform the test.