Your Textbook Has Emphasized That Testing Two Hypothesis Sequentially Is $H _ { 0 } : \beta _ { 5 } = 0 , \beta _ { 6 } = 0$

Essay

Your textbook has emphasized that testing two hypothesis sequentially is not the same as testing them simultaneously. Consider the following confidence set below, where you are testing the hypothesis that $H _ { 0 } : \beta _ { 5 } = 0 , \beta _ { 6 } = 0$ .

Your statistical package has also generated a dotted area, which corresponds to drawing
two confidence intervals for the respective coefficients.For each case where the ellipse
does not coincide in area with the corresponding rectangle, indicate what your decision
would be if you relied on the two confidence intervals vs.the ellipse generated by the F-
statistic.