(a (b (c (d (e [ == ) ) (f) (g (h ) (i) ) (k S DNA sequences from two different regions of two closely linked human fetal globin genes were studied by Weir (1996). The counts of nucleotides in 3'- flanking regions of the genes and Introns are reported in the table. Region | length [A] C [ G | T | 3'-flanking 1000 029| 015 0.26 | 030 T The question of equality of G nucleotides in 3'- flanking regions as compared to Introns, a synthesised part of the genes themselves. Suppose that these two regions are independent. Let the number of G nucleotides in 3'-flanking regions and Introns be X and Y , respectively. Suppose that Xand Y are binomial random variables with parameters (n,, p1) and (ny, p;). Determine (n*y, p*;) and (n*, p*,), the estimates of the unknown parameters (ny, p1) and (n,, p;), respectively. The null and alternative hypotheses are Hy: p1=p; and Ha:p1# pa, respectively. Interpret these hypotheses in terms of presence of nucleotide G in the regions of interest. Let the average number of G nucleotides in 3'- flanking regions and Introns be 1 1 X aX and Yoy, respectively. (i) Obtain the expected values of X and Y . (ii) Obtain the variances of X and Y. Write down the test statistic for testing Hg: p;=p; versus H,:p:# p,. What is the distribution of the test statistic under H, ? Provide the parameter(s) of the distribution. Observed Find the observed value of the test statistic. Test, Let the significance level @=0.01. Use your answer in (e) and obtain the critical value. Test the hypothesis Hy: py=p; versus Hg:p.# ps. Draw a conclusion. Run the relevant statistical test in R. Copy and paste the R-code and its output into \"YourFullIName.docx\". Hence validate your decision made in (i) based on the P-value to be found using Observed from (f). Test