Question

Yield strength of steel connecting bars. To protect against earthquake damage, steel beams are typically fitted and connected with plastic hinges. However, these plastic hinges are prone to deformations and are difficult to inspect and repair. An alternative method of connecting steel beams—one that uses high strength steel bars with clamps— was investigated in Engineering Structures ( July 2013). Mathematical models for predicting the performance of these steel connecting bars assume the bars have a mean yield strength of 300 megapascals (MPa). To verify this assumption, the researchers conducted material property tests on the steel connecting bars. In a sample of three tests, the yield strengths were 355, 369, and 350 MPa.Do the data indicate that the true mean yield strength of the steel bars exceeds 300 MPa? Assume the sample is drawn from a normally distributed population. Test using the p-value approach and = .01. State ?your conclusion in context.

Answer 1

Ho :   µ =   300                  
Ha :   µ >   300       (Right tail test)          
                          
Level of Significance ,    α =    0.01                  
sample std dev ,    s = √(Σ(X- x̅ )²/(n-1) ) =   9.8489                  
Sample Size ,   n =    3                  
Sample Mean,    x̅ = ΣX/n =    358.0000                  
                          
degree of freedom=   DF=n-1=   2                  
                          
Standard Error , SE = s/√n =   9.8489   / √    3   =   5.6862      
t-test statistic= (x̅ - µ )/SE = (   358.000   -   300   ) /    5.6862   =   10.20

                          
p-Value   =   0.0047   [Excel formula =t.dist(t-stat,df) ]              
Decision:   p-value<α, Reject null hypothesis                       

Conclusion: There is enough evidence the true mean yield strength of the steel bars exceeds 300 MPa                      

THANKS

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