H₀ : ₁ = ₂ H₁ : _{1 2}

A random sample of 9 observations from one population revealed a sample mean of 25 and a sample standard deviation of 4.0. A random sample of 4 observations from another population revealed a sample mean of 29 and a sample standard deviation of 4.6. 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.) The decision rule is to reject H₀ if t < ___ or t > ___.

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

c. Compute the test statistic. (Negative amount should be indicated by a minus sign. Round your answer to 3 decimal places.)