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) What distribution does the sample test statistic follow? Explain.
(b) State the hypotheses.
(c) Compute 1 - 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 μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.