Q.1. Select the best option/answer and fill in the appropriate box on the Answer Sheet. (20)

(i) The probability of event given the event B is P(A/B) is equal to P(A) if B is:

(a) any event in sample S (b) sample space S

(c) A ⊂B (d) B is dependent on A

(v) A student is attempting to log on internet with 0.5 chance of successful attempt in each trial. The

average number of attempts required to log on successfully is:

(a) 1 (b) 2 (c) 3 (d) 4

(viii) Let X be the number of patients arriving at OPD on any day in a hospital according to poison

distribution with the probability of at least one arrival in a day is

2

1 e − . Then average number of

arrivals of patients per day is:

(a) 8 (b) 4 (c) 2 (d) 1

(ix) To test the hypothesis Ho:μ1= μ2= μ3 at ∝= 0.05, then one can use:

(a) Regression Analysis (b) Analysis of Variance (c) z-test (d) t-test

(xi) The probability of accepting a hypothesis when it is false is 0.2 then the probability of rejecting

this hypothesis when it is false is:

(a) 0.95 (b) 0.9 (c) 0.85 (d) 0.8

(xii) If (x1, y1), ….. (xn, yn) set of n observations onVariable X = Hours studied, random variable Y =

test score and Y = a + bx is the least square line that approximates the regression of test scores on

the number of hours studied is given by Y = 21.819 + 3.471 X. If the desired test score is at least

60 then hours of studied should be at least:

(a) none (b) at most 10 (c) at least 10 (d) at least 11

(xv) For population with heterogeneous groups, the suitable sampling scheme is:

(a) Simple Random Sampling (b) Systematic Sampling

(c) Cluster Sampling (d) Stratified Sampling

(xvi) The variance of x, y, z, u, v objects is:

(a) 5 (b) 5 (c) 1 (d) none of these

(xvii) For a size of size n from ( )

2 2

õ , õ , μ N is unknown, Ho: μ= μoagainst H1: μ# μothen:

(a) t test with used be will 05 . 0 at d.f. 1 n ∝= −

(b) F test with used be will 05 . 0 at d.f. n ∝=

(c) t test with used be will 025 . 0 at d.f. 1 n ∝= −

(d) X

2

test with used be will 025 . 0 at d.f. 1 n ∝= −

(xviii) Height of date trees, say, follow N(8,4)then the third moment about mean is:

(a) 3×64 (b) 4×256 (c) 0×4 (d) none of these

(xix) In a sample of size n, x are girls with variance V(x) and n–x are boyswith variance is::

(a) V(x) (b) V(x) + n

2

(c) V(x) – n

2

(d) none of these

(xx) If two random variables are independent then correlation or covariance zero. If correlation or

covariance between two variables X and Y is zero then:

(a) X and Y are independent of one another (b) X and Y may be independent on one another

(c) X and Y may be mutually exclusive (d) None of these

(i) The probability of event given the event B is P(A/B) is equal to P(A) if B is:

(a) any event in sample S (b) sample space S

(c) A ⊂B (d) B is dependent on A

(v) A student is attempting to log on internet with 0.5 chance of successful attempt in each trial. The

average number of attempts required to log on successfully is:

(a) 1 (b) 2 (c) 3 (d) 4

(viii) Let X be the number of patients arriving at OPD on any day in a hospital according to poison

distribution with the probability of at least one arrival in a day is

2

1 e − . Then average number of

arrivals of patients per day is:

(a) 8 (b) 4 (c) 2 (d) 1

(ix) To test the hypothesis Ho:μ1= μ2= μ3 at ∝= 0.05, then one can use:

(a) Regression Analysis (b) Analysis of Variance (c) z-test (d) t-test

(xi) The probability of accepting a hypothesis when it is false is 0.2 then the probability of rejecting

this hypothesis when it is false is:

(a) 0.95 (b) 0.9 (c) 0.85 (d) 0.8

(xii) If (x1, y1), ….. (xn, yn) set of n observations onVariable X = Hours studied, random variable Y =

test score and Y = a + bx is the least square line that approximates the regression of test scores on

the number of hours studied is given by Y = 21.819 + 3.471 X. If the desired test score is at least

60 then hours of studied should be at least:

(a) none (b) at most 10 (c) at least 10 (d) at least 11

(xv) For population with heterogeneous groups, the suitable sampling scheme is:

(a) Simple Random Sampling (b) Systematic Sampling

(c) Cluster Sampling (d) Stratified Sampling

(xvi) The variance of x, y, z, u, v objects is:

(a) 5 (b) 5 (c) 1 (d) none of these

(xvii) For a size of size n from ( )

2 2

õ , õ , μ N is unknown, Ho: μ= μoagainst H1: μ# μothen:

(a) t test with used be will 05 . 0 at d.f. 1 n ∝= −

(b) F test with used be will 05 . 0 at d.f. n ∝=

(c) t test with used be will 025 . 0 at d.f. 1 n ∝= −

(d) X

2

test with used be will 025 . 0 at d.f. 1 n ∝= −

(xviii) Height of date trees, say, follow N(8,4)then the third moment about mean is:

(a) 3×64 (b) 4×256 (c) 0×4 (d) none of these

(xix) In a sample of size n, x are girls with variance V(x) and n–x are boyswith variance is::

(a) V(x) (b) V(x) + n

2

(c) V(x) – n

2

(d) none of these

(xx) If two random variables are independent then correlation or covariance zero. If correlation or

covariance between two variables X and Y is zero then:

(a) X and Y are independent of one another (b) X and Y may be independent on one another

(c) X and Y may be mutually exclusive (d) None of these

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