Model Question Paper HSE / Plus Two /12th Std / +2 : Statistics www.dhsekerala.gov.in

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Document Descdribed : Statistics Question Paper, Kerala Question Paper

Second Year Higher Secondray Model Examination
Part III
Statistics
Maximum : 60 Scores
Time : 2 Hours
Cool off time : 15 Minutes

http://dhsekerala.gov.in/ques_download.aspx
http://dhsekerala.gov.in/downloads/q...2_31_deepa.pdf

1.a)Who is the founder of indian statistical Institute
i) RA Fisher ii) W.S. Gosset
iii) Prof. Mahalnobis iv) Karl pearson
b) Write a short note on NSSO (1+2)
2. Check the continuity at x=1 of the function f(x)=2x, x<1 = x2+1, x?1 (3)
3. The cost function of a tyre manufacturing company is given by C(x)=x3-5x2+24x+200 3 2 where ‘x’ is the number of units prodused
a) Find the marginal cost function
b) Find the value of ‘x’ for which the cost is minimum
c) Find the minimum cost.
4. a) The factors that causes seasonal variations are
a) Climate, weather conditions, customs etc
b) Natural calamities, war etc
c) Change in business cycle
d) None of these
5. Let y= ex+x log x find dy and d2y dx dx2 (2)
6. a) Null hypothesis in ANOVA is
i) Variances are equal
ii) means are equal
iii) Both
iv) S.D are equal
8. The local body of a township installed 2000 elecric lamps having an average life of 1000 burning hours with a S.D of 200 hours
i) what number of lamps might be expected to fail in the first 700 burning hours?
ii) what percent of the lamps might be expected to fail between 500 to 800 hours? (4)
9. a) coefficient of correlation between two variables X and Y is 0.32. their covariance is 7.86. the variance of X is 10, find the S.D of Y. b) The following are the marks obtained by 7 students in Accountancy (X) and statistics (Y). complete the rank correlation between X and Y
7.a) In testing of Hypothesis, Power of the test is
i) P(type I error)
ii) I-P(type I error)
iii)P(type II error)
iv) I-P(type II error)
b) The mean weights of a sample of 10 people from a normal population was found to be 66 kilograms with a standard deviation of 3 kilograms.is it reasonable to believe that the average weights of the people of the locality is greater that 64 kgs (given ?= 0.05)
i) Specify H0 and H1
ii) Specify the test statistic and its distri bution
iii) What is the calculated value of the test statistics?
iv) what is the inference (1+5)
11. A manufacture producers two products X and Y . The first requires 3 hours for assembling and 4 hours for packing. The second requires 12 hours for assembling and 8 hours for packing. The plant has 60 hours for assemblings and 80 hours for packing.the profit margin for X is 7 and for Y is 21
i) Determine the objective function
ii) Determine the constraints
iii) Solve the LPP graphically
Mark in Accountancy(X) 72 78 64 61 59 70 85
Mark in Statistics (Y) 65 72 90 85 66 52 80 (3+4)
OR
10. a) Which of the following is true
i) bxy=0.8 bxy= -0.3 r= 0.49
ii) bxy= -0.8 byx= -0.3 r= 0.49
iii) bxy= - 0.8 byx= -0.3 r= -0.49
iv) bxy=0.8 byx=0.3 r= -0.49
b) From the follwing results, otain the two regression equations and estimate the yield of crops when rainfall is 29 cms
Y( Yeild in kgs) X(Rainfall in cms)
Mean 508.4 26.7
S.D 36.7 4.6
Coefficient of correlation between yield and rainfall is 0.52
14. The mean and variance of a Binomial distribution are 5 and 2 respectively.
i) Estimate the parameters n and p
ii) Also find P(x=1) (3)
15. Evaluate (4x+2) ?x2+x+1 dx (2)
OR
17. a) A population consists of the values 70,62,67,68,61 Take random samples of size 2 by SRSWOR
i) Show that sample mean is unbaised for population mean
ii) Find the variance of the sample mean
b) Let x1, x2,x3 be a random sample of size 3 taken from a population with mean and SD which of the following statistic is unbiased for ?
i) x1+x2-x3 ii) x1+x2+x3