State whether the following statements are true or false and briefly justify your answer. a. A 99% confidence interval for the slope 3 based on our data is calculated to be [-5,-2). Therefore, B must be negative. b. Under the same confidence level, the prediction interval of a new observation is always wider than the confidence interval for the corresponding mean response. c. If we assume that Y, is normally distributed, then Y, must also be normally distributed. d. Suppose we have knowledge of the true population parameters Bo, B, Bp. Given this information, we could estimate E(Y) perfectly. In other words, we can obtain the true E(Y). e. Suppose we have knowledge of the true population parameters Bo... Bp. Given this information, we could predict Y perfectly. f. Your classmate wants to test whether the regression coefficient related to X is equal to zero or not at a = 0.05. They set up the null and alternative as follows: Ho: B=0 versus H: B 0. 2 g. The constant variance assumption requires that , has constant variance.