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Unless otherwise specified, numerical answers should be corrected to two decimal places. Section A Multiple Choice Questions Answer ALL questions in this section. Each question carries 4 marks. 1. A company wants to know the production efficiency of its newly-invented machinery. Which of the following is the most appropriate way to collect the data? A. Experiment B. Observation 2. C Interview D. Statistical publication Which of the following is an advantage of secondary data? A. Limitations of documents B. Ready to use C. D. Relatively expensive Possible for violating copyright (20 marks) 3. There are 6 multiple choice questions in a test paper. Each question provides 4 answers for students to choose from. How many different possible outcomes can be made? A. 24 B. 720 C. 1296 D. 4096
4. The percentage increase in the Retail Price Index (RPI) from year 2015 to year 2021 is 8.8%. Taking year 2015 as the base period, the RPI of year 2021 is: A. 92 B. 108.8 C. 118.8 D. 128.8 5. The material usage of a factory for the past 3 years are recorded as below: Year Material usage 2019 2020 2021 The index number of 2021 by choosing 2019 as the base period: A. 76.07 B. 113.71 C. 121.64 D. 135.21 (kg) 2643 2890 3215 Section B Short Questions (35 marks) Answer ALL questions in this section. Each question carries 5 marks. 6. A survey is conducted to study the leisure activities of the SS students in a school. Students are classified according to the streams they studied. The following table shows the relevant figures of the survey. Stream Number of S5 students to be selected Total number of S5 students Business 13 30 50 (a) Which data collection method should be used to collect the data? (b) What is the population size of the survey? (c) Which sampling method is applied in the survey? Arts 9 Science 15 80 (2 marks) (1 mark) (2 marks)
7. The test results of 30 students are recorded as below. Suppose the 2nd student is set as the starting point and every 9th student is selected to form a sample element. Class no. 01 02 03 04 05 06 07 08 09 10 11 70 49 62 81 90 71 78 Marks 64 68 61 62 Class no. 16 17 18 19 Marks 12 13 14 15 49 60 59 65 28 29 30 20 21 22 23 24 25 26 27 55 60 87 95 61 61 64 58 87 44 57 70 45 65 77 (a) Which sampling method is used? (b) What is the disadvantage of using the method in (a)? (c) What is the sample mean? (1 mark) (2 marks) (2 marks) 8. A survey has been conducted to analyze the gender of 260 readers of newspapers A and B. Newspaper A Newspaper B 93 Female Male 57 43 67 (a) If a reader is chosen at random, find the probability that the reader is female. (2 marks) (b) If two readers are chosen at random, find the probability that they read the same (3 marks) newspaper.
9. A recent finding shows that the probability of giving birth to a girl is 0.57. Correct your answers to 4 decimal places. (a) A couple plan to have 2 children. Find the probability that both of the 2 children are boys? (2 marks) (b) Another couple plan to have 3 chilen. Find the probability that at least one of them is a gril? (3 marks) 10. A box contains 20 balls of different colours: 12 white, 5 yellow and 3 red. (a) If two balls are randomly selected from the box without replacement, what is the (2 marks) probability of getting two yellow balls? (b) If two balls are randomly selected from the box with replacement, what is the probability of getting two balls of the same colours? (3 marks)
11. The stock prices of Company A at the end of years 2016 to 2021 are presented in the following line graph. 64 62 6 Jun 54 July 52 2015 2017 2018 2009 2000 2001 2022 (a) By using year 2016 as the base period, calculate the simple price indexes for years 2016 to 2021. (3 marks) Simple Price Index Year 2016 2017 2018 2019 2020 2021 (b) By what percentage did the prices of stock decrease between years 2018 and 2021? (2 marks) 2016 12. A product is made up of ingredients X, Y and Z. Their monthly costs are shown in the following table. Calculate the simple composite index of ingredient costs by choosing June as the base period. (5 marks) Month Ingredient X Ingredient Y Ingredient Z May $2,500 $1,300 $1,500 $2,300 Stock Value (5) $2,600 $900 $1,200 $1,700 $2,200 Simple Composite Index
(45 marks) Section C Long Questions Answer ALL questions in this section. Each question carries 15 marks. 13. (a) Alvan, Bill and Cyrus will sit for a driving test. The probabilities of passing the test are 0.8, 0.5 and 0.3 for Alvan, Bill and Cyrus respectively. Correct your answers to 2 decimal places. (i) Find the probability that all of them pass the test. (ii) Find the probability that all of them fail the test. (iii) Find the probability that at leak one of them passes the test. (iv) Find the probability that exactly one of them passes the test. (b) A bag contains six $1 coins, eight $2 coins and eleven $5 coins and four $10 coins. A coin is taken out from the bag randomly, what is the expected value of the coin obtained? (3 marks) (3 marks) (3 marks) (3 marks) (3 marks)
14. Visitors of a theme park comprise local people (L) and overseas tourists (O). Records of the first 30 visitors coming to the park on a given day are provided: 01 02 03 04 05 06 07 08 09 10 LOLLLOLLOLO 11 12 13 14 15. LOL Sequence 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 Status of visitors OOLLOLLLL 0 L L L 0 The CEO of the park wants to know the extent of satisfaction of visitors towards the park's facilities by using the following two methods. Method I: 6 visitors are chosen randomly. Method II: 6 visitors are chosen randomly and proportionally from the two groups of visitors separately. Sequence Status of visitors (a) If Method I is used, (i) identify the sampling method. (1 mark) (ii) write down the sequence numbers of visitors being chosen by using the below random number table with the starting point row 1 column 4. (6 marks) (b) If Method II is used, (1) how many local visitors and overseas visitors should be chosen respectively? (2 marks) (ii) write down the sequence numbers of the visitors being chosen by using the below random number table with the starting point row 1 column 3. (6 marks) Random Number Table Column 0 3 9 1 2 1 3 6 3 2 2 3 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 Row 16 012056071 211 6 3 2 0 0 790 3560 7 19 124 40349110478 8 3 4 2 5 2 8 2 4 6 1 29 1 3 682 6 0 42 1 0 1 1 4 05 131 L L
15. The following table shows the prices and quantities of three products sold by a shop in 2020 and 2021. Product Candy Potato chip Bread 2020 Price ($) 23 15 54 Quantity 710 850 430 2021 Price (S) 31 18 92 Quantity 740 920 570 (a) Using 2020 as the base year, calculate the Laspeyres Price Index of 2021. (b) Using 2020 as the base year, calculate the Paasche Price Index of 2021. (c) Using the result in part (a) and (b), calculate the Fisher Price Index of 2021. (5 marks) (5 marks) (5 marks)