7278214.656 + 0.266878787287:7&7 a. For the regression, the 95% interval estimate for the intercept is [10.602, 18.710]. Calculate the standard error of the estimated intercept. [hint: use gt in R to find the critical t statistics - check out Oct.2 in Class R script; you can also use R as a calculator. ] b. From the regression output, the standard error for the slope coefficient is 0.081. Test the null hypothesis that the true slope, &2, is 0.25 (or less) against the alternative that the true slope is greater than 0.25 using the 10% level of significance. Show all steps of this hypothesis test, including the null and alternative hypotheses, and state your conclusion. [hint: use gt in R to find the critical t statistics - check out Oct.2 in Class R script] c. On the regression output, the automatically provided p-value for the estimated slope is 0.001. What is the meaning of this value? Use a sketch to illustrate your answer. [Note: label the calculated t statistics in your sketch] d. A member of the board of supervisors states that ACA should fall if we admit more students. Using the estimated equation and the information in parts (a)-(c), test the null hypothesis that the slope parameter &7 is zero, or positive, against the alternative hypothesis that it is negative. Use the 5% level of significance. Show all steps of this hypothesis test, including the null and alternative hypotheses, and state your conclusion. Is there any statistical support for the board e W el s s s il s B