The data in the file Concrete1 represents the compressive strength, in thousands

Question

The data in the file Concrete1 represents the compressive strength, in thousands of pounds per square inch (psi). of 40 sample of concrete taken two and seven days after pouring;

a. At the 0.01 level of signifcance, is there evidence that the mean strength is lower at two days than at seven days? Use hypotheses test for the difference between two means;

The data is provided below. All numbers are with decimals.

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

Explanation / Answer

We will use here Two sample t test as Ppilation standard deviation unknown here.

Using MINITAB:

Two-Sample T-Test and CI: Two days_1, Seven days_1

Two-sample T for Two days_1 vs Seven days_1

N Mean StDev SE Mean
Two days_1 40 2.991 0.496 0.078
Seven days_1 40 3.544 0.504 0.080

Difference = (Two days_1) - (Seven days_1)
Estimate for difference: -0.553
95% upper bound for difference: -0.367
T-Test of difference = 0 (vs <): T-Value = -4.95 P-Value = 0.000 DF = 78
Both use Pooled StDev = 0.4998

Here P-value < alpha=0.05. We reject null hypothesis and conclude that there is evidence that the mean strength is lower at two days than at seven days.

Hope this will helps you. God Bless You . Thanks :)

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