31 STATISTICS MQP 1.pdf

GOVERNMENT OF KARNATAKA KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD II PUC MODEL QUESTION PAPER – 1 (2024-25) STATISTICS (31) Time: 3 Hours (Total number of questions: 38)...

GOVERNMENT OF KARNATAKA KARNATAKA SCHOOL EXAMINATION AND ASSESSMENT BOARD II PUC MODEL QUESTION PAPER – 1 (2024-25) STATISTICS (31) Time: 3 Hours (Total number of questions: 38) Max. Marks: 80 Instructions: 1. Statistical table and graph sheets will be supplied on request. 2. Scientific calculators are allowed. 3. All working steps should be clearly shown. 4. For Section – A, only the first written answers will be considered for evaluation. 5. For questions having diagram, graph and map, alternative questions are given at the end of the question paper in a separate section for visually challenged students. SECTION – A I. Choose the most appropriate answer from the choices given: (5 X 1 = 5) 1) The births occurring to women of child bearing age is called a) Fertility b) Fecundity c) Mortality d) Longevity 2) Factor reversal test is satisfied by a) Laspeyre’s index number b) Marshall- Edgeworth’s index number c) Fisher’s index number d) Kelly’s index number 3) In a Bernoulli distribution, if q = 0.8, the standard deviation is a) 0.16 b) 0.8 c) 0.2 d) 0.4 4) Which of the following statements are correct? i) P(Type – I error ) = α (ii) P(Type – I error ) = 1 – α iii) P(Type – II error ) = β (iv) P(Type – II error ) = 1 – β a) i and iv b) i and iii c) ii and iv d) ii and iii 5) The cost associated with the maintenance of inventory until they are sold or used is a) Holding cost b) Shortage cost c) Setup cost d) Capital cost II. Fill in the blanks by choosing the appropriate answers given in the brackets: (5 X 1 = 5) ( 0, Strategy, 100, Point, Interval, np) 6) The value of the index number for the base year is __________. 7) The mean of a student’s t - distribution with parameter ‘n’ is _______. 8) If a single value is proposed as an estimate of the unknown parameter, it is _________ estimation. 9) In statistical quality control, _______ chart is used for number of defectives. 10) In a game, the pre-determined rule by which a player determines his course of action is called ________. III. Match the following: (5 X 1 = 5) 11) A B a. Size of the cohort i. Leptokurtic (β2 > 3) b. Paasche’s index number ii. A function of sample values c. Chi-square distribution curve iii. Downward bias d. Statistic iv. Replacement problem e. Matrix minima method v. Radix vi. Transportation problem 1 IV. Answer the following questions: (5 X 1 = 5) 12) Mention a method of obtaining vital statistics. 13) Which component of the time series is unpredictable? 14) Under what condition Poisson distribution tends to Normal distribution? 15) Define statistical hypothesis. 16) When is transportation problem said to be balanced? SECTION – B V. Answer any FIVE of the following questions: (5 X 2 = 10) 17) Mention two uses of time series. 18) Write two conditions for applying binomial expansion method of interpolation and extrapolation. 19) Find the mean of a hyper-geometric distribution whose parameters are a = 3, b = 9 and n = 4. 20) If X ~ N(μ, σ2), then write the distribution of and. 21) A random sample of size 36 is drawn from a population whose standard deviation is 3. Compute standard error of the sample mean. 22) Given: n = 10, s2 = 14.4 and σ2 = 16, compute the chi – square test statistic. 23) In statistical quality control, if = 4, determine the upper control limit for the c - chart. 24) If R = 3000 units/year, C1 = Rs 4/unit/year and C3 = Rs 60/order, then calculate the minimum average inventory cost. SECTION – C VI. Answer any FOUR of the following questions: (4 X 5 = 20) 25) Calculate the consumer price index number by using family budget method for the following data. Price (in Rs) Group Weight Base year Current year Food 3000 4200 30 Fuel 2500 3280 20 Clothing 2000 2160 10 Housing 3200 4000 30 Entertainment 1600 2000 10 Other 3000 3600 20 26) Interpolate the value of Y when X = 26 by using Newton’s advancing difference method. X 20 30 40 50 Y 72 202 557 1137 27) The probability that a team winning the game is 2/5. If this team plays in 6 games, then find the probability that it wins in i) all the games ii) one or more games. 28) Obtain the theoretical frequencies by fitting Poisson distribution for the number of mistakes per page from the following distribution. Number of mistakes per page 0 1 2 3 4 Number of pages 92 79 50 15 4 2  29) From a random sample of 64 students of PUC, 16 students were found wearing spectacles. Can we conclude at 5% level of significance that the proportion of students wearing spectacles is 20%? 30) Solve the following game by using dominance principle. Is the game fair? Player – B B1 B2 B3 A1 -1 5 6 Player – A A2 0 4 3 A3 -4 2 7 A4 -5 0 8 31) The purchase price of a machine is Rs 5000. Its maintenance costs and resale values are as follows: Years 1 2 3 4 5 Maintenance cost (in Rs) 100 200 330 510 860 Resale value (in Rs) 3000 2500 2000 1500 1000 What would be the optimum replacement period for the machine? VII. Answer any TWO of the following questions: (2 X 5 = 10) 32) In an institution, the weights of students follow normal distribution with mean 60 kg. and standard deviation 4.5 kg. If committee decides to consider the students with minimum weight of 62 kg., show that only 33% of the students got selected. 33) The following data represents the blood pressure of 5 persons before and after performing dhyana. B.P. before dhyana 100 97 92 94 95 B.P. after dhyana 96 98 90 91 93 Can we conclude at 5% level of significance that dhyana reduces blood pressure? 34) Given D3 = 0 and D4 = 2.115, write the control limits for R – chart. Sub-group number 1 2 3 4 5 6 Range 2 5 2 4 2 3 35) Solve the following linear programming problem graphically: Maximize Z = 6x + 10y Subject to constraints: x + y ≤ 8 x + 3y ≤ 18 and x, y ≥ 0 SECTION – D VIII. Answer any TWO of the following questions: (2 X 10 = 20) 36) Calculate gross reproduction rate and net reproduction rate for the following data and comment on the result. Age group Female Female Survival (in years) population births ratio 15 – 19 16000 480 0.91 20 – 24 14500 899 0.90 25 – 29 13000 650 0.90 30 – 34 11500 460 0.88 35 – 39 10000 300 0.87 40 – 44 8700 87 0.86 45 – 49 7500 30 0.85 3 37) Calculate the Marshall-Edgeworth’s and Dorbish-Bowley’s price index numbers from the following data. Items Base year Current year Price (in Rs) Quantity Price (in Rs) Quantity A 17 10 25 14 B 22 12 29 17 C 30 13 24 22 D 41 12 47 15 38) a) Estimate the trend values by four yearly moving averages for the following time series data. Year 2015 2016 2017 2018 2019 2020 2021 2022 2023 Value 16 18 16 24 20 30 26 34 40 b) Fit a straight line trend equation of the form y = a + bx to the data given below. Year 2010 2012 2014 2016 2018 2020 2022 Production (in ‘000 quintals) 80 90 92 83 94 99 92 SECTION - E (For Visually challenged students only) 35) A tailor gets a profit of Rs.100 from a shirt and Rs. 170 from a pant. In a week from available 56 hours, he uses 36 hours for cutting and 20 hours for stitching. For cutting he requires 2 hours for a shirt and 3 hours for a pant. He requires 1 hour for stitching a shirt and 2 hours for stitching a pant. Formulate an L.P.P. ******* 4