This problem is partially based on problem 12.5b & 12.5c from Lomax & Hahs-Vaughn, 3rd ed.

Is the following contrast legitimate? $\displaystyle {H}_{{0}}:{\left(\mu_{{2}}+\mu_{{4}}\right)}-{\left(\mu_{{1}}+\mu_{{3}}+\mu_{{5}}\right)}={0}$ Question for reflection:  Why or why not?

Using the same means, what coefficients might be used to alter the contrast to yield a legitimate contrast? $\displaystyle {H}_{{0}}:$  $\displaystyle \cdot{\left(\mu_{{2}}+\mu_{{4}}\right)}-$ $\displaystyle \cdot{\left(\mu_{{1}}+\mu_{{3}}+\mu_{{5}}\right)}={0}$

1st coefficient:  Preview Question 6 Part 1 of 2  
2nd coefficient:  Preview Question 6 Part 2 of 2