The following sample data have been collected from a paired sample from two populations. The claim is that the first population mean will be at least as large as the mean of the second population. This claim will be assumed to be true unless the data strongly suggest otherwise.

Sample 1 Sample 2 Sample 1 Sample 2 4.4 3.7 2.6 4.2 2.7 3.5 2.4 5.2 1.0 4.0 2.0 4.4 3.5 4.9 2.8 4.3 2.8 3.1

a. State the appropriate null and alternative hypotheses.

b. Based on the sample data, what should you conclude about the null hypothesis? Test using a  0.10.

c. Calculate a 90% confidence interval for the difference in the population means. Are the results from the confidence interval consistent with the outcome of your hypothesis test? Explain why or why not.