The null and alternate hypotheses are:

H₀:₁=₂

H₁:₁₂

A random sample of 12 observations from one population revealed a sample mean of 25 and a sample standard deviation of 4.5. A random sample of 8 observations from another population revealed a sample mean of 30 and a sample standard deviation of 3.5.

The population standard deviations are unknown but assumed to be equal. At the 0.01 significance level, is there a difference between the population means?

Required:

a.State the decision rule.(Negative amounts should be indicated by a minus sign. Round your answer to 3 decimal places.)

b.Compute the pooled estimate of the population variance.(Round your answer to 3 decimal places.)