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GCE JUN 2007 : AS, S2: Statistics2

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ADVANCED General Certificate of Education 2007 Mathematics assessing Module S2: Statistics 2 AMS41 Assessment Unit S4 [AMS41] WEDNESDAY 20 JUNE, AFTERNOON TIME 1 hour 30 minutes. INSTRUCTIONS TO CANDIDATES Write your Centre Number and Candidate Number on the Answer Booklet provided. Answer all eight 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. 1 24.3.06RTS 2 19.7.06BP 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 AMS4S7 2244 1 24.3.06RTS 2 19.7.06BP BLANK PAGE AMS4S7 2244 2 [Turn over Answer all eight questions. Show clearly the full development of your answers. Answers should be given to three significant figures unless otherwise stated. 1 Miss White is taking a random sample of ten students from a population of eighty-five students. She has assigned each student a two digit code number from 01 to 85. Then she uses a spreadsheet package to produce an array of random digits as shown in Fig. 1 below. Miss White starts at the top left of the table and reads horizontally in order to obtain her sample. 0 6 9 1 9 5 3 2 1 8 8 7 4 6 1 6 6 2 7 1 0 7 8 7 7 1 9 7 5 7 4 5 8 4 1 6 5 6 5 2 8 0 7 4 9 6 4 8 5 0 8 0 5 3 3 4 0 4 5 7 7 6 7 3 9 3 9 3 0 2 8 8 7 5 4 4 2 6 6 7 1 2 1 2 Fig. 1 [4] 1 24.3.06RTS 2 19.7.06BP Showing clearly your method, find the code numbers of the students in the sample. AMS4S7 2244 3 [Turn over 2 Mr Brown s Year 10 class have just finished their end of term examinations. The results of a random sample of ten pupils performances in IT and English are given in Table 1 below and shown in the scatter diagram in Fig. 2 below. Table 1 Student A B C D E F G H I J IT Mark 49 71 80 75 86 43 78 78 64 55 English Mark 59 65 74 84 84 86 70 85 71 53 Scatter diagram of English vs IT 90 English 80 70 60 50 40 50 60 70 80 90 IT Fig. 2 The product moment correlation coefficient for these data is 0.37 Mr Brown concludes that there is weak positive correlation between performance in IT and performance in English. [3] 1 24.3.06RTS 2 19.7.06BP (i) Explain why Mr Brown s conclusion might not be sound. AMS4S7 2244 4 [Turn over Table 2 below contains the results of a different random sample of ten students in IT and Mathematics. The difficulty in part (i) does not apply here. Table 2 Student K L M N O P Q R S T IT Mark (x) 64 78 46 84 60 75 39 72 52 80 Mathematics Mark (y) 75 68 71 77 50 47 54 53 40 47 Summary statistics for these data are: x = 650 y = 582 x2 = 44386 y2 = 35462 xy = 38125 (ii) Find the product moment correlation coefficient for these data. (iii) Comment on the value obtained in part (ii). 3 [5] [2] In an experiment the times, x minutes, taken by a random sample of forty teachers to complete a sudoku puzzle were recorded. The summary statistics are given below: x = 408.3 x2 = 4381.51 Assume Normality of the population distribution. (i) Calculate an estimate for the population variance. [2] (ii) Find a 90% confidence interval for the mean time to complete the puzzle. [5] 1 24.3.06RTS 2 19.7.06BP (iii) Other than changing the sample size, what change would produce a wider confidence interval? [1] AMS4S7 2244 5 [Turn over 4 Dr Green has a very large number of tracks stored on her computer for use with her MP3 player. She makes CDs for listening to in the car by copying ten tracks selected at random. If X is the random variable the length, in minutes, of a track stored on the computer , then X ~ N (4.2,1.6). (i) Write down the mean and variance of X10, the mean track length on a CD. (ii) Find the probability that a CD chosen at random has mean track length less than 4 minutes. [5] (iii) How would the answer to (ii) be affected if the number of tracks on the CD were decreased? Explain your answer. 5 [2] [2] An experiment is carried out to explore the percentage of fat in chips cooked at different temperatures. (i) Which is the independent variable in this experiment? Give a reason. [2] In a separate experiment the percentage of fat ( y) is considered in relation to the thickness (in mm) of the chips (x). The summary values of the data are given below: x = 244 y = 302 x2 = 3054.3 y2 = 4584.86 xy = 3719.32 n = 20 (ii) Find the least squares regression equation for percentage of fat on thickness. (iii) Estimate the mean percentage of fat for chips of thickness 12.5 millimetres. 2 19.7.06BP 1 24.3.06RTS [2] (iv) What assumptions do you think were made in carrying out the experiment for (ii)? 6 [6] [2] The manufacturer of a brand of spaghetti is suspected of filling the packets with less than the 500 grams stated on the label. A random sample of 10 packets was taken and the mass of spaghetti, in grams, in each is as follows: 501.8 496.2 498.7 500.6 499.1 496.8 502.1 495.3 Assuming Normality, test at 5% level whether the suspicion is justified. AMS4S7 2244 6 495.8 498.6 [12] [Turn over 7 The random variable X is Normally distributed with mean . A random sample of 50 observations of X produced the following summary statistics: x = 1456 x2 = 42440 Test at 5% level the following hypotheses: H0: = 29.5 H1: 29.5 8 [8] Mr Black makes pre-packed sandwiches. The thickness of the bread that he uses is Normally distributed with mean 10 millimetres and variance 1.6 millimetres2 The thickness of the filling is Normally distributed with mean 12 millimetres and variance 2.8 millimetres2 (i) Find the mean and variance of the thickness of Mr Black s sandwiches. (Mr Black makes his sandwiches with the filling between two square slices of bread.) [3] In order to package his sandwiches Mr Black cuts the sandwich diagonally into two triangles, sets the two halves one on top of the other and places them inside a triangular plastic container. (ii) Write down the mean and variance of the combined thickness of the sandwich triangles before placing in the container. [2] The maximum thickness that the container can accommodate is 65 millimetres. Mr Black sometimes has to compress the sandwich slightly to fit it into the container. Sandwiches requiring more than 10% compression are unusable. (iii) Find the percentage of sandwiches that are unusable. 1 24.3.06RTS 2 19.7.06BP THIS IS THE END OF THE QUESTION PAPER AMS4S7 2244 7 [7] 2 19.7.06BP 1 24.3.06RTS S 3/06 0000 7-041-1 [Turn over

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Additional Info : Gce Mathematics June 2007 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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