Question 5.18: The article "Direct Strut-and-Tie Model for Prestressed Deep...
The article “Direct Strut-and-Tie Model for Prestressed Deep Beams” (K. Tan, K. Tong, and C. Tang, Journal of Structural Engineering, 2001: 1076-1084) presents measurements of the nominal shear strength (in kN) for a sample of 15 prestressed concrete beams. The results are
\begin{array}{llllllll}580 & 400 & 428 & 825 & 850 & 875 & 920 & 550 \\575 & 750 & 636 & 360 & 590 & 735 & 950 &\end{array}
1s it appropriate to use the Student’s t distribution to construct a 99% confidence interval for the mean shear strength? If so, construct the confidence interval. If not, explain why not.
To determine whether the Student’s t distribution is appropriate, we will make a box plot and a dotplot of the sample. These are shown in the following figure.
There is no evidence of a major departure from normality; in particular, the plots are not strongly asymmetric, and there are no outliers. The Student’s t method is appropriate.
We therefore compute \bar{X} = 668.27 and s = 192.089. We use expression (5.14) with n = 15 and α /2 = 0.005. From the t table with 14 degrees of freedom, we find t_{14..005} = 2.977. The 99% confidence interval is 668.27 \pm(2.977)(192.089) / \sqrt{15}, or (520.62, 815.92).
\bar{X}\pm t_{n-1, \alpha / 2}\frac{s}{\sqrt{n}} (5.14)
