申論題

4. (18%) A sports statistician studied the relation between the time (Y, in seconds) for a competitive swimming event and the swimmer's age (X, in years) for 20 swimmers with ages ranging from 8 to 18. The statistician employed a quadratic regression model (Yᵢ = a+bXᵢ +cXᵢ² + εᵢ) and obtained the following results:
Ŷ=147.3-11.11X + 0.2730X² and s = 0.1157

(4-C) Test whether the curvature effect can be dropped from the quadrant regression model,controlling the α risk at 0.05. State the alternatives, the decision rule, the value of the test statistic, and the conclusion. What is the P-value of the test? (10%)