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Q1. The following results were obtained from medical records about age (x) and systolic blood pressure (y) of a group of 10 women: The mean and variance of x are 53 and 121 respectively and mean and variance of y are 142 and 169 respectively. S(x-X)(y-Y)=1210. (X is the mean of x and Y is mean of y). Find the regression equation of systolic blood pressure on age of a women. Also estimate systolic blood pressure of a women whose age is 55. While solving this example, explain the relevant terms used in details. (10 Marks)
Q2. A sarcastic graduate student from Waterloo was testing the American media at the Salt Lake City Olympics about Canadian history and geography. Reporters were given a 10- item multiple-choice questionnaire to complete. Each question had four possible answers. Unfortunately, one reporter wanted to return to the bar for the rest of the morning, so he simply guessed on all of the questions and then handed in the questionnaire. What is the probability that he will score at least 6 out of 10 in this questionnaire? State clearly the assumptions you need to make to solve this question. Also, write a note on the relevant probability distribution you used to solve this example. (10 Marks)
Q3. In order to compare the batting performances in Test Cricket of Indian legends, in a meeting of administrators it was proposed that instead of using arithmetic mean of runs scored in all the innings played, Median score be used as an average to represent the performance. But one member, who happened to be a statistician, objected to the proposal saying that by doing so we are favouring the players like Sachin Tendulkar.
a) Give your opinion with appropriate justification. (5 Marks)
b) If it is further decided to compare the performance based on consistency in performance, which statistical measures would you recommend? Substantiate your answer with appropriate justification.