1.A study has been conducted to investigate the association between type II diabetes and incidence of chronic kidney disease (CKD). 100 people with type II diabetes and 100 people with no diabetes were recruited into the study and followed up for 10 year. The participants had normal kidney function at recruitment and the primary outcome was whether the patients develop chronic kidney disease during follow-up.

The dataset contains 200rows (one row per patient) and three columns-Subject: subject number (not to be used in analysis)-Diabetes coded with 1 if the patient had type 2 diabetes at recruitment and 0 if the patient had no diabetes at recruitment-CKD coded with1 if the participant has developed CKD during follow-up and zero otherwise.

(i)At the 5% level of significance test for an association between Diabetes and CKD incidence.

(ii)Calculate a 95% confidence interval for the difference in proportions of patients with CKD in the diabetic vs non-diabetic group.

(iii)Compare the results under points (i) and (ii) and formulate the conclusion.

Answerthe following: a} Show that the exponerrtial distribution has a lack of memory.-r and the minimum property,r b} What are the characteristic properties of the Poisson input process? Discuss some of their limitations by giving examples from practical queueing systems. c} Suppose there are 2 types of customers arriving at the same server according to independent Poisson processes. Show that the aggregate arrival process is still a Poisson process. Time left 1:16:39 Question 18 A continuous-time Markov chain (CTMC) has the following @ = (qi; ) matrix (all rates are transition/second) Not yet answered Marked out of 0 18 63 0 2.00 17 0 41 0 Q = (qij) = Flag 21 0 0 94 question 0 0 5 0 Is this CTMC a Birth-Death process? ONo, it is not birth-death process OYes, it is birth-death process Next page Previous pageQuestion 13 The Mann-Whitney and the Wilcoxon tests are both used to compare the means of Not yet answered Two populations. Which of these should be used if the samples are related? Marked out of 1.00 Flat question Select one: a. Wilcoxon b Mann-Whitney "C neither d. . both of these may be used Previous page MAT1114 - Statistics trimester 1 2019 Jump to Alternative A exam and solutions100 . Median 025-75 I 5-95% 60 Percentage of chorus 40- 201 Calling Singing Calling Singing Sympatric Allopatric (PRF) (Riske Creek) Mountain chickadees Download : Download full-size image Figure 4. Percentage of time that mountain chickadees from the sympatric (with black-capped chickadees) population (sympatric-MOCH; Wilcoxon test: P= 0.01) and the allopatric population (allopatric-MOCH; Wilcoxon test: P= 1) spent calling versus singing during the dawn chorus