Chapter 10.2, Problem 9P

Basic Computation: Testing- ${\mu }_1-{\mu }_2$ A random sample of 49 measurements from a population with population standard deviation 3 had a sample mean of 10. An independent random sample of 64 measurements from a second population with population standard deviation 4 had a sample mean of 12. Test the claim that the population means are different. Use level of significance 0.01.

(a) Check Requirements What distribution does the sample test statistic follow ? Explain.

(b) State the hypotheses.

(c) Compute ${\bar{x}}_{{}_1}-{\bar{x}}_{{}_2}$ and the corresponding sample test statistic.

(d) Find the P-value of the sample test statistic.

(e) Conclude the test.

(f) Interpre t the results.

(g) Find a 99% confidence interval for ${\mu }_1-{\mu }_2$. Explain the meaning of the confidence interval in the context of the problem.