Question

The slant shear stress test is widely used for evaluating the bond of resinous repair materials to concrete. This test utilizes cylindrical specimens that are made of two identical halves bonded at 30 degrees. It was reported by a study in the ACI Materials Journal, 1996 titled “Testing the bond between repair materials and concrete substances” that for 12 specimens prepared using wire brushing, the mean shear strength is 19.20 N/mm2 and the standard deviation is 1.58 while for hand-chiseled specimens, the value of the mean and standard deviation are 23.13 N/mm2 and 4.01 respectively. Using confidence levels of 90%, 95% and 99%, does the true mean seem to be the same for the two methods. Clearly state your hypothesis statement and steps.

Answer 1

Let's denote the data for wire brushing specimens group by subscript 1 and the other by 2.

Data given is:

Sample means, m1 = 19.20, m2 = 23.13

Sample Standard deviation, s1 = 1.58, s2 = 4.01

Sample sizes, n1 = n2 = 12

Hypotheses are:

H0: Mean is same for two groups, 1 = 2

Ha: Mean is not same for two groups, 1 2

We calculate standard error:

S = ((s1^2)/n1 + (s2^2)/n2)^0.5 = ((1.58^2)/12 + (4.01^2)/12)^0.5 = 1.244

The 90% CI is:

(m2-m1)-(1.64*S) < < (m2-m1)+(1.64*S)

(23.13-19.20)-(1.64*1.244) < < (23.13-19.20)+(1.64*1.244)

1.89 < < 5.97

The 95% CI is:

(m2-m1)-(1.96*S) < < (m2-m1)+(1.96*S)

(23.13-19.20)-(1.96*1.244) < < (23.13-19.20)+(1.96*1.244)

1.49 < < 6.36

The 99% CI is:

(m2-m1)-(2.58*S) < < (m2-m1)+(2.58*S)

(23.13-19.20)-(2.58*1.244) < < (23.13-19.20)+(2.58*1.244)

0.72 < < 7.14

Thus we see that none of the above intervals contains the value zero.

So the true mean does not seem to be the same for the two methods.