The data in the accompanying table represent the compressive​ strength, in thousands of pounds per square inch​ (psi), of 20 samples of concrete taken two and seven days after pouring.

Question

Sample	Two days	Seven days
1		2.985	3.475
2		2.830	3.505
3		3.425	4.030
4		2.060	2.945
5		2.895	2.915
6		2.205	2.280
7		3.115	3.675
8		2.935	3.630
9		3.765	4.570
10		2.630	2.850
11		3.800	4.070
12		2.750	3.250
13		2.830	3.340
14		3.335	3.580
15		2.495	3.230
16		3.080	3.140
17		3.160	3.430
18		3.590	3.915
19		3.760	4.130
20		2.005	2.690

(0.01 significance)

What is the TSTAT?

Answer 1

Hi Ruman A.,

It looks as if you are perhaps being asked to assess if the 7-day compressive strengths are correlated to the 2-day compressive strengths. But, if I recall, a compressive strength is a destructive test -- it crushes the sample. So then how could the same sample be used for both a 2- and a 7-day strength test? Or, if a single coring was sliced to make several smaller samples for (individual) testing, then why worry about that correlation -- worry first, if the replicate samples at the same time point correlate well! If you don't have that, then testing different slices just isn't telling you much.

Also, if these samples are being used to assess the integrity of a large poured slab (for example), are the samples useful for the 7-day point? They have been removed from their location, and (I hope) stored under a standard condition of temperature and humidity -- but how do you know that is what obtained in the poured slab?

Or perhaps (more likely, if you are clueless in an introductory course?), you are being asked for a "Student's" (it's named after a person of that name) t test -- test for the significance of the difference of the means of 2 populations (here, 2-day vs. 7-day data). That you should be able to easily look up; you will need the mean, and the standard deviation of each population. Then use the table to index for these (it may run using a derived variable which relates the means and their difference to the two standard deviations and their difference and the population size(s))..

-- Cheers, -- Mr. d.