Refer to Exercise 2.58, where \(n_{1}=30\) specimens of \(2 \times 4\) lumber have \(\bar{x}=1,908.8\) and \(s_{1}=327.1\) psi. A second sample of size \(n_{2}=40\) specimens of larger dimension, \(2 \times 6\), lumber yielded \(\bar{y}=2,114.3\) and \(s_{2}=472.3\). Test, with \(\alpha=0.05\), the null hypothesis of equality of mean tensile strengths versus the one-sided alternative that the mean tensile strength for the second population is greater than that of the first.

Data From Exercise 2.58

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2.58 Modern computer software programs have come a long way toward removing the tedium of calculating statistics. MINITAB is one common and easy-to-use program. We illustrate the use of the computer us- ing MINITAB commands. Other easy-to-use programs have a quite similar command structure. The lumber used in the construction of buildings must be monitored for strength. Data for the strength of 2 x 4 pieces of lumber in pounds per square inch are in the file 2-58.TXT. We give the basic commands that calculate n, x, and s as well as the quartiles. The session commands require the data to be set in the first column, C1, of the MINITAB work sheet. The command for creating a boxplot is also included.