The null and alternate hypotheses are: H₀ : ₁ = ₂ H₁ : _{1 2} A random sample of 8 observations from one population revealed a sample mean of 23 and a sample standard deviation of 2.5. A random sample of 9 observations from another population revealed a sample mean of 25 and a sample standard deviation of 1.3. The population standard deviations are unknown but assumed to be equal. At the 0.05 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.)

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

d. State your decision about the null hypothesis. multiple choice 1

• Do not reject H₀.
• Reject H₀.

e. The p-value is multiple choice 2

• between 0.1 and 0.05.
• less than 0.001.
• between 0.02 and 0.05.
• between 0.001 and 0.01.
• between 0.1 and 0.2.