T200275ummeriexam - STZ X . Home / TWltiel 6 9 C' Q @ httsz/leameewcentraHeprodefleeIOIexythosleamcloudflare.b|ackboardcdn_com/5cf - - 9 III\\ E] 0 A @ 5 D E Welcome, CORMAC e 5 Google 0 YouTuhe is FUT Web App , EA SP... Li Email , REDMOND, c... 8 timetable @ harryhesketh , Twitch . Soccer Streamer Ofci... O OneDrive Other Bookmarks ED 'MJ,| 4lof6 l+ 80% v 9:11 ll Question 3 (25 Marks) " A randomised Controlled trial was undertaken to compare sleep deprivation over an eight week period between those using sleep therapy [i.e. the intervention] and usualecare [i.e. the controls]. One hundred adults were randomly assigned to the intervention or control arm. The primary response variable was whether the person demonstrated an improvement in sleep deprivation (Le. a success] after eight weeks. At the end of the trial 26 out of 50 in the control group showed an improvement after 8 weeks. whereas this happened for 36 out of the 50 in the intervention group. Let the random variable X denote the number ofsuccesses in the 711 individuals receiving the intervention where it is assumed that X is generated from a Binomial distribution with parameter 91 and that the random variable Y denotes the number of successes in the g individuals receiving standard care where it is assumed that Y is generated from a Binomial distribution with parameter 92. Assume that X and I' are independent and that E : \"i and 5; : n1 1 z and that the joint likelihood function for 91 and 62 is as follows: L091. 92; x) = (:1) era 7 80'\" (1:) 92y (1 7 99\"\" a. Use this likelihood function to construct the joint likelihood function. [5 Marks] b. Use the maximum likelihood estimators of 81 and 92 in terms ofthe observed data to construct the Hessian matrix. [8 Marks] c. Construct a 95% Wald Condence Interval for 81 92. [5 Marks] d. Interpret this interval to form a conclusion on the effectiveness of the intervention in the population of interest [2 Marks] e. What concerns might you have using the Wald Approach to generate a 95% Condence Interval for 91 7 92. [3 Marks] f. Why would an interval estimate for log 9 be worth considering? [2 Marks] v z ._ ENG 09 ' . . [I E ii a '0 Type harem 593\"" )3 1 GA 25,105,203 E1