Chapter 10.2, Problem 10P

Basic Computation: Testing ${\mu }_1-{\mu }_2$ Two populations have normal distributions. The first has population standard deviation 2 and the second has population standard deviation 3. A random sample of 16 measurements from the first population had a sample mean of 20. An independent random sample of 9 measurements from the second population had a sample mean of 19. Test the claim that the population mean of the first population exceeds that of the second. Use a 5% level of significance.

(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) Interpret the results.

(g) Find a 90% confidence interval for ${\mu }_1-{\mu }_2$ Explain the meaning of the confidence interval in the context of the problem.