The slant shear test is widely accepted for evaluating the bond of resinous repa

Question

The slant shear test is widely accepted for evaluating the bond of resinous repair materials to concrete; it utilizes cylinder specimens made of two identical halves bonded at 30 degree. An article reported that for 12 specimens prepared using wire-brushing, the sample mean shear strength (N/mm^2) and sample standard deviation were 18.60 and 1.59, respectively, whereas for 12 hand-chiseled specimens, the corresponding values were 22.17 and 4.04. Does the true average strength appear to be different for the two methods of surface preparation? State and test the relevant hypotheses using a significance level of 0.05. (Use mu_1 for wire-brushing and mu_2 for hand-chiseling.) Calculate the test statistic and determine the P-value. (Round your test statistic to two decimal places and your P-value to three decimal places.) t = P- value =

Explanation / Answer

Formulating the null and alternative hypotheses,              
              
Ho:   u1 - u2   =   0  
Ha:   u1 - u2   =/   0  
At level of significance =    0.05          
As we can see, this is a    two   tailed test.      
Calculating the means of each group,              
              
X1 =    18.6          
X2 =    22.17          
              
Calculating the standard deviations of each group,              
              
s1 =    1.59          
s2 =    4.04          
              
Thus, the standard error of their difference is, by using sD = sqrt(s1^2/n1 + s2^2/n2):              
              
n1 = sample size of group 1 =    12          
n2 = sample size of group 2 =    12          
Thus, df = n1 + n2 - 2 =    22          
Also, sD =    1.253318927          
              
Thus, the t statistic will be              
              
t = [X1 - X2 - uD]/sD =    -2.848436996   [ANSWER, TEST STATISTIC]

*************************************
Also, using p values, as this is two tailed,          
              
p =    0.009345892   [ANSWER, P VALUE]
***********************************

*****************************************************

Hi! If you use another method/formula in calculating the degrees of freedom in this t-test, please resubmit this question together with the formula/method you use in determining the degrees of freedom. That way we can continue helping you! Thanks!

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.