Please answer all parts in detail:

A random sample of twenty five STAT 231 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:

Y.- = a + 3361- + R.-, where Ri~ G[0, 0'), i = 1, 2, ...., 25; independent Some estimates based on the data are given below: \"a = 3.94, = 1.05, 33 = 164.192, 331x.- = 1,854, 53 = 50.75138 a} Test the hypothesis that there is no relationship between the rst quiz mark and the second quiz mark. State the null and alternative hypotheses. Calculate the observed value of the test statistic that would be used to test Ho (versus the two-sided alternative]. Be sure to state the distribution of the test statistic, assuming H0 is true. Include the degrees of freedom of the test statistic, if needed. You do NOT need to calculate the p-value in this part of the question. That will be done in part b). b] Using R and the result from part a], calculate the appropriate p-value in order to test Ho: [3 = 0 [versus the two-sided alternative]. You must include the R code used for the calculation