1026 The data in represent the compressive strength in thous

10.26 The data in represent the compressive

strength, in thousands of pounds per square inch (psi), of 40 samples of concrete taken two and seven days after pouring. Source: Data extracted from O. Carrillo-Gamboa and R. F. Gunst,

“Measurement-Error-Model Collinearities,” Technometrics, 34, 1992,

pp. 454–464.

a. At the 0.01 level of significance, is there evidence that the mean strength is lower at two days than at seven days?

b. What assumption is necessary about the population distribution in order to perform this test?

c. Find the p-value in (a) and interpret its meaning.

Sample   Two Days   Seven Days

1   2.83        3.505

2   3.295   3.43

3   2.71        3.67

4   2.855   3.355

5   2.98        3.985

6   3.065   3.63

7   3.765   4.57

8   3.265   3.7

9   3.17        3.66

10   2.895   3.25

11   2.63        2.85

12   2.83        3.34

13   2.935   3.63

14   3.115   3.675

15   2.985   3.475

16   3.135   3.605

17   2.75      3.25

18   3.205   3.54

19   3        4.005

20   3.035   3.595

21   1.635   2.275

22   2.27        3.91

23   2.895   2.915

24   2.845   4.53

25   2.205   2.28

26   3.59        3.915

27   3.08        3.14

28   3.335   3.58

29   3.8        4.07

30   2.68        3.805

31   3.76        4.13

32   3.605   3.72

33   2.005   2.69

34   2.495   3.23

35   3.205   3.59

36   2.06        2.945

37   3.425   4.03

38   3.315   3.685

39   3.825   4.175

40   3.16        3.43

Solution