Please answer all parts in detail:

Please solve them without using the probability table.

Q: A random sample of twenty five students was taken in order to investigate whether or not there is a relationship between the second quiz mark (Y) and the first quiz mark (x). The relationship is modeled using the following:

a) Construct a 99% confidence interval for a. You must use R to determine the appropriate value of the quantile needed in the 99% confidence interval for a. b) Consider the hypothesis test: Ho: a = 0 ( versus the two-sided alternative). Based on the confidence interval in part a), would you expect your p-value to be less than 1% or greater than 1%? Explain. c) Construct a 90% prediction interval for the mark on the second quiz for a student that scored 72 on the first quiz. You must use R to determine the appropriate value of the quantile needed in the 90% prediction interval.Y1- = a + Bx!- + Rt, where R1 ~ C(O, c], i = 1, 2, ...., 25; independent Some estimates based on the data are given below: \"a = 3.94, 3: 1.05, s: = 164.192, 331le = 1,854. 5,? = 50.75138