Saturday, 25 March 2017

HSST Statistics Solved Paper SR For SC/ST 16/2017/OL - Part 4

61.       "Simple random sampling" is the technique of drawing a sample in such a way that each unit of the population has
(A) distinct and dependent chance of being included in the sample
(B) distinct but independent chance of being included in the sample
(C) an equal but dependent chance of being included in the sample
(D) an equal and independent chance of being included in the sample
Answer: D
62.       In SRSWR with usual notations, the standard error of the sample mean `quadbary` is
(A) `quadS({N-n}/{Nn})^{1/2}`
(B) `quadS({N-1}/{Nn})^{1/2}`
(C) `quadS(1-{n}/{N})^{1/2}`
(D) `quadS/n(1-{1}/{N})^{1/2}`
Answer: B
63.       The formulae for optimum allocation in various strata in stratified sampling were first derived by
(A) Tschuprov
(B) Cochran
(C) Lahiri
(D) Neymann
Answer: A
64.       The ratio estimator of population mean is unbiased if sampling is done according to
(A) PPSWR
(B) PPSWOR
(C) SRSWR
(D) SRSWOR
Answer: A
65.       The cluster sampling is more efficient when
(A) the variation within clusters in more
(B) the variation between clusters is less
(C) both (A) and (B)
(D) neither (A) nor (B)
Answer: C
66.       Local control is a device to maintain
(A) homogeneity within blocks
(B) homogeneity among blocks
(C) both (A) and (B)
(D) neither (A) nor (B)
Answer: A
67.       In a linear model `quadY_{ij}=alpha_i+e_{ij},` `quadj=1,2,...,n_i;` `quadi=1,2,...,k,` consider
(i) `quadalpha_1-3alpha_2+alpha_3+alpha_4`
(ii) `quadalpha_1+3alpha_2-alpha_3-alpha_4`
(iii) `quadalpha_1+3alpha_2-2alpha_3-2alpha_4`
Then which of the following is correct?
(A) (i) and (ii) are linear contrasts
(B) (i) and (iii) are linear contrasts
(C) (ii) and (iii) are linear contrasts
(D) (i), (ii) and (iii) are linear contrasts
Answer: B
68.       While analyzing the data of a `quadkxxk` Latin Square Design, the degrees of freedom in the ANOVA is
(A) `quadk^2-1`
(B) `quadk-1`
(C) `quadk^2-2k+1`
(D) `quad(k-1)(k-2)`
Answer: D
69.       In a split plot design with factor `quadA` at 3 levels in main plots, factor `quadB` at 3 levels in sub-plots and 3 replications, the degrees of freedom for sub-plot error is
(A) 27
(B) 12
(C) 8
(D) 4
Answer: B
70.    If the interactions `quadAB` and `quadBC` are confounded with incomplete blocks in a `quad2^n` factorial experiment, then automatically confounded effect is
(A) `quadA`
(B) `quadC`
(C) `quadAC`
(D) `quadABC`
Answer: C

71.    Which among the following is a consistent estimator of the population mean when samples are from the Cauchy population?
(A) Sample mean
(B) Sample median
(C) Sample variance
(D) None of these
Answer: B
72.    If the regularity conditions of the CR inequality are violated then the least attainable variance will be
(A) equal to the CR bound
(B) greater than the CR bound
(C) less than the CR bound
(D) zero
Answer: C
73.    A method to obtain the UMVUE is by using
(A) Rao-Blackwell Theorem
(B) Baye's Theorem
(C) Neymann-Pearson Theorem
(D) Lehmann-Scheffe Theorem
Answer: D
74.    A complete-sufficient statistic for `p` in the Bernoulli distribution
`(x, p) = p^x (1-p)^x; x=0, 1.
= 0 `"otherwise"` is
(A) The first order statistic `X_{(1)}`
(B) The `n` `"^{th}"` order statistic `X_{(n)}`
(C) `sum_(i=1)^n X_i`
(D) `X_{(n)}-X_{(1)}`
Answer: C
75.    The least square estimators are
(A) Unbiased
(B) BLUE
(C) UMVUE
(D) All these
Answer: D
76.    A 95% confidence interval for λ, when a large sample is taken from a Poisson population with parameter λ is
(A) `bar x ``+- 1.65``sqrt(( bar x)/(n)) `
(B) `lambda+- 1.65 sqrt((lambda)/(n)) `
(C) `bar x+- 1.96sqrt((bar x)/(n)) `
(D) `lambda +- 1.96sqrt((lambda)/(n)) `
Answer: C
77.    The minimum Chi-squared estimators are not necessarily
(A) Unbiased
(B) Consistent
(C) Efficient
(D) Asymptotically normal
Answer: A
78.    Which one of the following statements is true?
(A) Even if the UMP test does not exist, a UMPU test may exist
(B) Even if the UMPU test does not exist, a UMP test may exist
(C) A UMP test exists only if a UMPU test exists
(D) A UMPU test exists only if a UMP test exists
Answer: A
79.    In paired `t` test the two random variables should be
(A) Paired and uncorrelated
(B) Unpaired and correlated
(C) Both paired and correlated
(D) Neither paired nor correlated
Answer: C
80.    With usual notations, the criterion for acceptance in SPRT is
(A) `lambda_m <= ((1-beta))/(alpha) `
(B) `lambda_m >= ((1-beta))/(alpha) `
(C) `lambda_m <=(beta)/((1-alpha)) `
(D) ` lambda_m >= (beta)/((1-alpha)`
Answer: C

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