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) 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 99% confidence interval for μ1 - μ2. Explain the meaning of the confidence interval in the context of the problem.