Refer to Exercise 5.
Consider the following summary data on the modulus of elasticity (× 106 psi) for lumber of three different grades [in close agreement with values in the article "Bending Strength and Stiffness of Second-Growth Douglas-Fir Dimension Lumber" (Forest Products J., 1991: 35-43), except that the sample sizes there were larger]:

Use this data and a significance level of .01 to test the null hypothesis of no difference in mean modulus of elasticity for the three grades?
Compute a 95% t CI for θ = 1/2(µ1 + µ2) - µ3?

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