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GCE JUN 2006 : AS, S2: Statistics2

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ADVANCED General Certificate of Education 2006 Mathematics assessing Module S2: Statistics 2 AMS41 Assessment Unit S4 [AMS41] MONDAY 19 JUNE, MORNING 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 log e z AMS4S6 847 Answer all seven questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 The resistance of a thermistor changes with temperature. A new type of thermistor is being tested by finding values of the resistance at different temperatures. The results are given in Table 1 below. Table 1 Temperature ( C), x Resistance (Ohms), y 12 15 18 20 22 23 25 28 30 33 90.0 88.1 85.7 84.1 82.0 81.5 80.0 77.8 75.9 73.5 Summary statistics, which you may find useful, are: x = 226 y = 818.6 x2 = 5504 y2 = 67261.06 xy = 18185.5 (i) Find the equation of the least squares regression line of resistance on temperature. [6] (ii) Use your equation to estimate the mean resistance of thermistors at 27 C. [2] AMS4S6 847 2 [Turn over 2 Paul is exploring the belief that older conductors conduct more slowly. He looks up information on various performances of Wagner s Der Ring des Nibelungen and his findings are summarised in Table 2 and illustrated in Fig. 1 below. Table 2 45 53 51 36 64 73 59 46 Performance time (mins), y 918 932 930 942 935 943 931 922 Performance Time (mins) Age (years), x 945 940 935 930 925 920 915 30 40 50 60 Age (years) 70 80 Fig. 1 The product-moment correlation coefficient for these data is 0.37 (i) How might Paul interpret this value? [2] Paul decides to treat the value pair (36, 942) as an outlier. The summary statistics for the remaining seven value pairs are given below. x = 391 y = 6511 x2 = 22457 y2 = 6056567 xy = 364156 (ii) Calculate the product-moment correlation coefficient for these seven pairs of values. [6] (iii) What conclusion might Paul now make? [2] (iv) Suggest a way that Paul could improve his method of exploration. [1] AMS4S6 847 3 [Turn over 3 A sample of forty-five chocolates is tested for the amount of sugar, x grams, that they contain. The summary values are given below. x = 571 x2 = 7260 (i) Calculate an unbiased estimate for the variance of the amount of sugar in these chocolates. (ii) Calculate a 95% confidence interval for the mean amount of sugar in these chocolates. [6] (iii) Explain what the answer in part (ii) means. 4 [2] [2] A Normal variable, X, has mean 40 and standard deviation 5 A sample of 40 observations of X is taken. (i) Write down the distribution of X, the mean of the 40 observations. (ii) Find P(X > 41.5) [5] (iii) Find a such that P( X 40| < a) = 0.7 | 5 [3] [5] The masses of the contents in tins of beans are Normally distributed with mean 430 grams and standard deviation 4 grams. The masses of the tin containers are also Normally distributed with mean 20 grams and standard deviation 0.3 grams. Find the probability that the total mass of two tins of beans is greater than 909 grams. 6 [8] The label on a particular brand of coffee states that the mass of coffee in the jar is 200 grams. A sample of 80 jars of coffee had a mean of 198.6 grams and sample standard deviation 5 grams. Carry out a suitable test to decide if jars of this coffee contain less than 200 grams. AMS4S6 847 4 [10] [Turn over 7 Ten 400-metre runners train in the morning and in the evening. On a particular day their times are recorded. The results are given in Table 3 below. Table 3 Runner A B C D E F G H I J Morning time (seconds) 51.4 55.8 53.7 57.6 53.3 52.4 59.4 53.7 52.0 56.6 Evening time (seconds) 52.1 56.7 53.1 57.5 52.9 51.8 60.0 53.3 51.7 56.1 Carry out a suitable test to decide if there is any difference in the runners performances in the morning and in the evening. [15] THIS IS THE END OF THE QUESTION PAPER AMS4S6 847 5 [Turn over S 6/05 4000 302507(48)

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Additional Info : Gce Mathematics June 2006 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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