Chapter 8.5, Problem 12P

Basic Computation: Testing μ₁ ‒ μ₂ 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.

1. (a) Check Requirements What distribution does the sample test statistic follow? Explain.
2. (b) State the hypotheses.
3. (c) Compute $\bar{x}$₁ ‒ $\bar{x}$₂ and the corresponding sample distribution value.
4. (d) Find the P-value of the sample test statistic.
5. (e) Conclude the test
6. (f) Interpret the results.