CSS Statistics Past Paper 2020

Instructions specific to this paper

• Attempt ONLY FOUR questions from PART-II by selecting TWO questions from EACH
• Use of Calculator is allowed.
• Use of statistical table is allowed.
• Find mean and standard deviation.
• Find and describe x ± 2( sd )

Questions

1. Q. 210 marks

   (a) Two bags A and B contain red and blue marbles. Bag A contains 7 red and 8 blue marbles. Bag B contains 9 red and 7 blue marbles. One bag is selected randomly and one marble is drawn. If the drawn marble is red then what is the probability that this drawn marble is from bag A? (b) For the given set of observations showing weekly sale of a specific type of refrigerators. (10) (20) 35, 56, 43, 21, 43, 56, 78, 12, 56, 47, 76, 23, 52 (i) Find mean and standard deviation. (ii) Find and describe x ± 2( sd )

2. Q. 320 marks

   Raw material used in the production of a synthetic fiber is stored in a place that has no humidity control. Measurements of the relative humidity (y) and moisture control (x), on ten days, are given below. Fit a Least Square model: y = β1 + β 2 x. Further find and explain coefficient of determination. Humidity 46 53 37 42 34 29 60 48 41 48 Moisture 12 14 11 13 10 8 17 12 10 15

3. Q. 420 marks

   Three teaching methods were implemented to a homogenous group of school level students. Groups of students, selected randomly, were taught with a particular method and their scores were recorded as given below: Method A 94, 88, 91, 74, 87, 97 Method B 85, 82, 79, 84, 61, 72, 80 Method C 89, 67, 72, 76, 69 Use Kruskal-Wallis Test, at 5% level of significance to test the hypothesis that, on average there is no significant difference between the average score of these teaching methods.

4. Q. 515 marks

   (a) Draw all possible samples of size 3, without replacement, from the population, 6, 12, 3, 9, 15, and 21. Find sample means and prove the following relationships, using usual notations. σ2  N −n (i) E ( x ) = µ and ( ) (ii) V x =   n  N −1  (b) Define Stratified Random sampling method, identify situations where this type of (5) (20) sampling is beneficial. Give an example. STATISTICS

5. Q. 615 marks

   (a) To compare the effectiveness of two medicines M1 and M2, for headache, a study was conducted. Samples from a homogeneous group of headache patients were selected randomly and administered M1 (six patients) and M2 (8 patients) selected randomly. Recovery times (in minutes) of Patients were recorded as follows: Medicine M1 12 9 8 11 10 9 Medicine M2 5 11 7 6 8 6 5 4 Could it be concluded at 5% level of significance that, on average, medicine M2 is better than M1? (b) While testing hypothesis one may commit errors when we make decisions. State and (5) (20) explain such errors, supporting by real life example.

6. Q. 715 marks

   (a) The following Latin Square layout displays the scores secured by nine college students. Students are of different ethnic background and various professional interests. Professional Ethnic Background Interest X Y Z Law A B C 75 86 69 Medicine B C A 95 79 86 Engineering C A B 70 83 93 In this table A, B, and C are the three instructors. Analyze and test following hypotheses, Use α = 0.05. (i) Having a different instructor has no effect on the scores. (ii) Differences in ethnic backgrounds have no effect on the scores (iii) Differences in professional interest have no effect on the scores. (b) Describe the role of Multiple Comparison tests in Analysis of Variance. Name few (5) (20) Multiple Comparison tests and explain one method.

7. Q. 85 marks

   (a) Explain the terms Demography and Vital statistics. List few sources of demographic data both locally and globally. (b) Using the information given in the following table. Calculate Total Fertility Rate (TFR) (10) and Gross Fertility Rate (GFR). Age No of births to (years) Women Population women 15-19 84790 343 20-24 70010 14541 25-29 72660 16736 30-34 75920 12218 35-39 75100 756 40-44 71620 82 45-49 66660 45 (c) Differentiate between Rates and Ratios. Explain Crude Death Rate and Specific Death (5) (20) Rate.

Standard FPSC instructions

Printed on this and every CSS paper.

• Part-II is to be attempted on the separate Answer Book.
• All the parts (if any) of each question must be attempted at one place instead of at different places.
• Write Q. No. in the Answer Book in accordance with Q. No. in the question paper.
• No page/space be left blank between the answers. All the blank pages of the Answer Book must be crossed.
• Extra attempt of any question or any part of the attempted question will not be considered.