Plus Two HSC 12th Std +2 Statistics Sample Question Paper : www.dge.tn.gov.in

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Document Described : Statistics Question Paper, Tamil Nadu Question Paper

GOVT. MODEL QUESTION PAPER
STATISTICS
12TH STD. MAX. MARKS : 150
TIME : 3 HOURS

PART I (50 MARKS)
Note : (1) Answer all questions.
(2) Each question carries one mark 50 x 1 = 50
Choose the best answer :
1. When two events A and B are mutually exclusive, then P (AÇB) is
(a) 1 (b) 0 (c) P(A) . P(B) (d) None of these
2. An integer is chosen from 1 to 20. the probability that the number is divisible by 4 is
(a) 1/4 (b) 1/3 (c) 1/2 (d) 1/10

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3. In tossing three coins at a time, the probability of getting atmost one head is
(a) 3/8 (b) 7/8 (c) 1/2 (d) 1/8
4. The probability of two persons being born on the same day in an ordinary year
(ignoring date)
(a) 1/49 (b) 1/365 (c) 1/7 (d) 1/366
6. Probability of drawing a spade queen from a well shuffled pack of cards is
(a) 1/13 (b) 1/52 (c) 4/13 (d) 8/13
7. If P(A) = 0.4, P(B) = 0.5 and P(AÇB) = 0.2 then P(B/A) is
(a) 1/2 (b) 1/3 (c) 4/5 (d) 2/5
9. The distribution of height of persons in a country is a random variable of the type :
(a) Continuous random variable (b) Discrete random variable
(c) Neither discrete nor continuous (d) Continuous as well as discrete random variable random variable
10. Var (5x + 2)
(a) 25 var (x) (b) 5 var (x) (c) 2 var (x) (d) 25
11. A random variable x has E(x) = 2 and E (x2) = 8, its variance is
(a) 4 (b) 6 (c) 8 (d) 2
13. If X is a random variable with its mean `x, the expression E(x-`x)2 represents
(a) the variance of x
(b) second central moment
(c) both (a) and (b)
(d) none of (a) and (b)
14. If X is a random variable, E(etx) is known as
(a) characteristic function
(b) moment generating function
(c) probability generating function
(d) none of these
15. For Bernoulli distribution with probability p of a success and q of a failure, the relation between mean and variance that hold is
(a) mean < variance (b) Mean > variance
(c) mean = variance (d) None of the above
16. X is a Binomial Variate with mean = 4, variance = 4/3, then, P (x = 0) is
(a) (2/3)6 (b) (2/3)5 (1/3) (c) (1/3)6 (d) 35 (2/3)6
17. An approximate relation between Q.D, M.D. and S.D. of normal distribution is
(a) 10: 12 : 15 (b) 12 : 10 : 15 (c) 15 : 12 : 10 (d) 10 : 15 : 12
18. The mean of normal distribution is 60, then mode is equal to
(a) 60 (b) 40 (c) 50 (d) 30
19. The mean and variance of a binomial distribution b (5, 1/3) is
(a) 5/3 & 10/9 (b) 5/2 & 10/6 (c) 5/3 & 10/6 (d) 5/2 & 10/9
21. In normal distribution skewness is
(a) one (b) zero (c) 3 (d) -1
22. In normal distribution the value of Kurtosis is
(a) 1 (b) 3 (c) -3 (d) 0
23. The area p (-¥ < Z < 0) is
(a) 1 (b) 0.1 (c) 0.5 (d) 0
24. The hypothesis may be classified as
(a) Simple (b) Composite
(c) Null (d) All of the above
25. Critical value of |Zµ| at 5% level of significance for two tailed test is
(a) 1.645 (b) 2.33 (c) 2.58 (d) 1.96
26. H0 is rejected when H0 is true is
(a) Type II error (b) Type I error
(c) Simple error (d) none of the above
27. Whether a test is one sided or two sided depends on
(a) alternative hypothesis (b) composite hypothesis
(c) null hypothesis (d) simple hypothesis
30. The standard deviation of the sampling distribution is called
(a) Probable error (b) Standard error
(c) Sampling error (d) Non-sampling error
33. While testing the significance of the difference between two sample mean in case of small samples, the degrees freedom is
(a) n1 + n2 (b) n1 + n2 – 1 (c) n1 + n2 – 2 (d) n1 + n2 + 2
34. Equality of two population variances can be tested by
(a) t-test (b) F-test (c) c2-test (d) None of the above
35. Paired t-test is applicable, when the observations in the two samples are
(a) Paired (b) Correlated
(c) Equal in number (d) all the above
36. Degrees of freedom for chi-square in case of contingency table of order 4 x 3 are
(a) 12 (b) 9 (c) 6 (d) 8
38 The values of observed frequencies and expected frequencies are all equal then the value of c2 is
(a) -1 (b) +1 (c) >1 (d) 0
39. In the case of one-way classification with N observations and `t’ treatments, the degrees of freedom for error is
(a) N – 1 (b) t – 1 (c) N – t (d) Nt
40. Analysis of variance utilises
(a) F-test (b) c2 – test (c) Z-test (d) t-test
41. With 90, 35, 25 as SST, SSR and SSC respectively in case of two-way
classification, SSE is
(a) 50 (b) 40 (c) 30 (d) 20
42. A time series consists of
(a) two components (b) three components
(c) four components (d) five components
43. The component of a time series attached to long term variations is termed as
(a) cyclic variation (b) secular trend
(c) irregular variation (d) all the above
44. Business forecasts are made on the basis of
(a) Present data (b) Past data
(c) Polices and circumstances (d) All the above
46. With the two attributes the total number of class frequencies is
(a) Two (b) Four (c) Eight (d) Nine
47. In case of two attributes A and B the class frequency (AB) = 0 the value of Q is
(a) 1 (b) -1 (c) 0 (d) -1 £ Q £ 1
48. A business who is said to be averse to risk
(a) Prefers to take large risks to earn large gains.
(b) Prefers to act any time the expected monetary value is positive
(c) Avoids all situations but those with very high expected values.
(d) None of these
49. The criterion which selects the action for which maximum pay-off is lowest is known as
(a) Max – min criterion
(b) Min – max criterion
(c) Max – max criterion
(d) None of these
50. Decision theory is concerned with
(a) the amount of information that is available.
(b) Criteria for measuring the `goodness’ of a decision.
(c) Selecting optimal decision in sequential problems
(d) All the above

PART II : (30 MARKS)
Note : (1) Answer any 15 questions
(2) Each question carried 2 marks 15 x 2 = 30
51. State the axioms of probability
52. Find the probability that a leap year selected at random will contain 53 Sundays.
56. Comment on the following: ‘ The mean of a binomial distribution is 5 and its variance is 9’ .
57. Find the Binomial distribution whose mean is 3 and the variance is 2.
58. State any four properties of normal distribution.
59. In a test of significance, the calculated value is less than the critical value. What is your inference?
60. State type – one error and type – two error.
61. What `test statistic’ is to be used to find the test of significance for the
following problem? `1000 articles from a factory A are examined and found to have 3% defectives. 1500 similar articles from a second factory B are found to have only 2% defectives. Can it be reasonably concluded that the product of the first factory is inferior to the second’ ?
62. State the assumptions of students t – test
63. Explain the term ` degrees of freedom’ .
64. What are the precautions are necessary while applying chi-square test?
65. What are the components of time series?
66. Write any two merits and demerits of semi – average method.
67. Write the Yule’ s coefficient of association.
68. Verify whether the given data N = 100 (A) = 75, (B) = 60, and (AB) = 15 are consistent.
69. Explain the statistical decision theory.
71. An urn contains 5 red and 7 green balls. Another urn contains 6 red and 9 green balls. If a ball is drawn from any one of the two urns, find the probability that the ball drawn is green.
72. A random variable X has the density function f(x) = Ax2, 0 < x < 1. Determine A and find the probability between 0.2 and 0.5
73. Eight coins are tossed simultaneously. Find the probability of getting atleast six heads.
74. Suppose on an average 1 house in 1000 in a certain district has a fire during a year. If there are 2000 houses in that district, what is the probability that exactly 5 houses will have a fire during the year? (e-2 = 0.1353)
75. A car company decided to introduce a new car whose mean petrol
consumption is claimed to be lower than that of the existing car. A sample of 50 new cars we taken and tested for petrol consumption. It was found that mean petrol consumption for the 50 cars was 30 km per litre. Test at 5% level of significance whether the company’ s claim that he new car petrol consumption is 28 km per litre on the average is acceptable.

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The probability of two persons being born on the same day in an ordinary year
(ignoring date)
(a) 1/49 (b) 1/365 (c) 1/7 (d) 1/366

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