Question

2. The data set (Concrete1.xlsx) contains the compressive strength, in thousands of pounds per square inch (psi), of 30 samples of concrete taken two and seven days after pouring. (You need to use The Paired Difference Test).

(a) At the 0.10 level of significance, is there evidence of a difference in the mean strengths at two days and at seven days?

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

(c) At the 0.10 level of significance, is there evidence that the mean strength is lower at two days than at seven days?

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

Sample	Two Days	Seven Days
1	2.830	3.505
2	3.295	3.430
3	2.710	3.670
4	2.855	3.355
5	2.980	3.985
6	3.065	3.630
7	3.765	4.570
8	3.265	3.700
9	3.170	3.660
10	2.895	3.250
11	2.630	2.850
12	2.830	3.340
13	2.935	3.630
14	3.115	3.675
15	2.985	3.475
16	3.135	3.605
17	2.750	3.250
18	3.205	3.540
19	3.000	4.005
20	3.035	3.595
21	1.635	2.275
22	2.270	3.910
23	2.895	2.915
24	2.845	4.530
25	2.205	2.280
26	3.590	3.915
27	3.080	3.140
28	3.335	3.580
29	3.800	4.070
30	2.680	3.805

Answer 1

a) From the given data

Sample	Two Days	Seven Days	Difference
1	2.83	3.505	-0.675
2	3.295	3.43	-0.135
3	2.71	3.67	-0.96
4	2.855	3.355	-0.5
5	2.98	3.985	-1.005
6	3.065	3.63	-0.565
7	3.765	4.57	-0.805
8	3.265	3.7	-0.435
9	3.17	3.66	-0.49
10	2.895	3.25	-0.355
11	2.63	2.85	-0.22
12	2.83	3.34	-0.51
13	2.935	3.63	-0.695
14	3.115	3.675	-0.56
15	2.985	3.475	-0.49
16	3.135	3.605	-0.47
17	2.75	3.25	-0.5
18	3.205	3.54	-0.335
19	3	4.005	-1.005
20	3.035	3.595	-0.56
21	1.635	2.275	-0.64
22	2.27	3.91	-1.64
23	2.895	2.915	-0.02
24	2.845	4.53	-1.685
25	2.205	2.28	-0.075
26	3.59	3.915	-0.325
27	3.08	3.14	-0.06
28	3.335	3.58	-0.245
29	3.8	4.07	-0.27

From the differences,

Mean:

H0: there is no difference in the mean strengths at two days and at seven days
H1: there is difference in the mean strengths at two days and at seven days

i.e.

(B) 4) Using P-value:

Thus we conclude that there is difference in the mean strengths at two days and at seven days

c) H0: the difference the mean strength is lower at two days than at seven days
H1: the difference the mean strength is not lower at two days than at seven days

d) p-value: 0.00

since P-value < alpha 0.10 so we reject H0

Thus we conclude that the difference the mean strength is lower at two days than at seven days