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GCE JUN 2010 : AS, S2: Statistics2

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ADVANCED General Certificate of Education 2010 Mathematics assessing Module S2: Statistics 2 AMS41 Assessment Unit S4 [AMS41] FRIDAY 18 JUNE, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. You are permitted to use a graphic or scientific calculator in this paper. INFORMATION FOR CANDIDATES The total mark for this paper is 75 Figures in brackets printed down the right-hand side of pages indicate the marks awarded to each question or part question. A copy of the Mathematical Formulae and Tables booklet is provided. Throughout the paper the logarithmic notation used is ln z where it is noted that ln z logez 5266 BLANK PAGE 5266 2 [Turn over Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 An experiment is carried out to explore the relationship between the heights of twenty-year-old men and the heights of their fathers. Eight pairs are measured. The results are given in Table 1 below. Table 1 Height of son, x (cm) 176 162 187 158 165 170 193 153 Height of father, y (cm) 172 172 178 160 161 167 191 160 Summary values for these data are: n x y x2 y2 xy 8 1364 1361 233 936 232 343 233 000 (i) Calculate the product moment correlation coefficient for these data. (ii) Comment on the value obtained in part (i). 5266 [5] [1] 3 [Turn over 2 In linear regression, one of the variables is called the response or dependent variable. (i) Explain clearly what this means. Illustrate your answer with an example. [3] Eamon carries out an experiment to explore the link between the percentage of carbon monoxide (CO) in the exhaust fumes of a car and the number of revolutions per minute (RPM) of the engine. (ii) Give and briefly explain one modelling assumption for this experiment. [2] Eamon s data is given in Table 2 below. Table 2 RPM, x 1000 1500 2000 2500 3000 3500 % CO, y 1.17 1.9 2.86 3.37 3.98 4.45 Summary values for these data are: n x y x2 y2 xy 6 13 500 17.73 34 750 000 60.1583 45 680 (iii) Find the regression equation of percentage CO on RPM. (iv) If the car was running at 2200 RPM, estimate the percentage CO in the exhaust fumes. 5266 [6] [2] 4 [Turn over 3 Edith monitors the journey time, x minutes, of trains. She suspects that the regular train from Belfast to Bangor does not take the thirty minutes that it should. Her sample data is summarised below. n = 60 x = 1721 x2 = 49 441 (i) Calculate the mean and variance of the data. [3] (ii) Test Edith s suspicion at 5% level. 4 [10] Gareth is about to calculate a 95% confidence interval for the mean duration of telephone calls, duration x mins, made from his office. (i) Explain carefully what the expression 95% confidence interval means. [2] (ii) What modelling assumption is Gareth making in calculating the confidence interval? [1] Gareth s data for his sample is summarised below. n = 45 x = 339 x2 = 2799 (iii) Find the mean and variance of the call durations. (iv) Find a 95% confidence interval for the mean call duration. 5266 [3] [5] 5 [Turn over 5 Ten Year 8 Mathematics students are selected to test the effectiveness of a computer program designed to improve performance in Mathematics. They begin by taking a Mathematics examination. Next they follow a three month course using the computer program. Finally they take a similar Mathematics examination at the end of the course. The program makers claim that the students scores should improve by 10. The results of the examinations are given in Table 3 below. Table 3 Student A B C D E F G H I J Initial Score 56 67 48 70 38 66 54 70 45 51 Final Score 63 75 61 74 51 75 67 73 53 62 Test the program makers claim at 5% level. 6 7 [15] A continuous random variable X has mean 35 and variance 12 Sixty observations on X were taken at random. Find the probability that the sample mean is less than 34.7 [6] The independent random variables X and Y are such that X ~ N(20, 6) and Y ~ N(25, 4). Find: (i) P(X + Y > 43); [4] (ii) P(3X < 2Y). [7] THIS IS THE END OF THE QUESTION PAPER 5266 6 [Turn over 5266

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Additional Info : Gce Mathematics June 2010 Assessment Unit S4 Module S1: Statistics2
Tags : General Certificate of Education, A Level and AS Level, uk, council for the curriculum examinations and assessment, gce exam papers, gce a level and as level exam papers , gce past questions and answer, gce past question papers, ccea gce past papers, gce ccea past papers

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