A plant manager has collected productivity data for a sample of workers, intending to see whether there is a difference in the number of units they produce on Monday versus Thursday. The results (units produced) are in given data . Using the 0.01 level of significance, evaluate the null hypothesis that there is no difference in worker productivity between the two days. Identify and interpret the p-value for the test, then construct and interpret the 99% confidence interval for the mean difference in productivity between the days.