Suppose you fit the second-order model y = b0 + b1x + b2x2 + e to n = 25 data points. Your estimate of b2 is bn 2 = .47, and the estimated standard error of the estimate is .15.

a. Test H0: b2 = 0 against Ha: b2 ≠ 0. Use a = .05.

b. Suppose you want to determine only whether the quadratic curve opens upward; that is, as x increases, the slope of the curve increases. Give the test statistic and the rejection region for the test for a = .05. Do the data support the theory that the slope of the curve increases as x increases? Explain.