Seven manufacturing companies agreed to implement a time management program in hopes of improving productivity. The times, in minutes, it took the companies to produce the same quantity and type of part are listed below. Does this information indicate the program decreased production time? Assume normal population distributions. Use α= 0.05. Company 1 2 3 4 5 6 7
Before(1) 75 112 89 95 80 105 110
After(2) 70 110 88 100 80 100 99

Required:
a. What is the level of significance? State the null and alternate hypothesis. Find or estimate the P-value. Sketch the sampling distribution to show the area corresponding to the P-value.
b. Based on your answers above, will you reject or fail to reject the null hypothesis? State the conclusion in the context of the problem.