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Statistical Assistant Gr II-Statistical Invesigator Gr II-Computer Operator Gr II in Economics - Statistics question paper 2015

Date of test
21-04-2015
Question paper code
5/2015/OL
Category No.
165/2012
Questions
100
Answer key
Provisional Answer Key
Exam mode
Online (computer based)

Provisional key. Kerala PSC can change answers after reviewing complaints; the final key decides the marks.

Source: Kerala PSC (keralapsc.gov.in) · official document· Last updated 25 Sept 2026· How we check content

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As published by the Kerala Public Service Commission.

All 100 questions with answers

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  1. 1.
    S N D P Yogam was established in the year
    Show answer and explanation
    Answer: A —
    1903
    SNDP Yogam was established in 1903 under the leadership of Sree Narayana Guru.
  2. 2.
    Which one of the following is not a fundamental right ?
    Show answer and explanation
    Answer: B —
    Right to property
    Right to property was removed from the list of fundamental rights by the 44th Amendment Act, 1978.
  3. 3.
    The Article related with special privilege of Jammu and Kashmir
    Show answer and explanation
    Answer: A —
    Article 370
    Article 370 of the Indian Constitution granted special autonomous status to Jammu and Kashmir.
  4. 4.
    Who was the founder of Sadhu Jana Paripalana Sangham ?
    Show answer and explanation
    Answer: D —
    Ayyankali
    Ayyankali founded the Sadhu Jana Paripalana Sangham in 1907 to work for the upliftment of the depressed classes.
  5. 5.
    The temple entry proclamation of 1936 was issued by
    Show answer and explanation
    Answer: B —
    Sri Chithira Thirunal
    The Temple Entry Proclamation was issued by Maharaja Chithira Thirunal Balarama Varma of Travancore.
  6. 6.
    The poem 'Jathikkummi' was written by
    Show answer and explanation
    Answer: D —
    Pandit K P Karuppan
    Pandit K. P. Karuppan wrote the poem 'Jathikkummi' to protest against the caste system.
  7. 7.
    The Malayalam novelist who used the pen name 'Vilasini'
    Show answer and explanation
    Answer: A —
    M K Menon
    M. K. Menon, a prominent Malayalam novelist, wrote under the pen name 'Vilasini'.
  8. 8.
    Human Rights Day is celebrated on
    Show answer and explanation
    Answer: C —
    December 10
    Human Rights Day is observed every year on December 10, the day the UN General Assembly adopted the Universal Declaration of Human Rights.
  9. 9.
    The father of White Revolution in India
    Show answer and explanation
    Answer: C —
    Varghese Kurian
    Dr. Verghese Kurien is known as the father of the White Revolution in India for his role in Operation Flood.
  10. 10.
    ISRO Space craft 'Mangalayan' entered in the martian orbit in ____
    Show answer and explanation
    Answer: D —
    24 September 2014
    ISRO's Mars Orbiter Mission (Mangalyaan) successfully entered Martian orbit on 24 September 2014.
  11. 11.
    Who is the founder of social networking site 'Facebook' ?
    Show answer and explanation
    Answer: C —
    Mark Zuckerberg
    Mark Zuckerberg is the founder of Facebook.
  12. 12.
    In which District Edakkal caves are situated ?
    Show answer and explanation
    Answer: B —
    Wayand
    Edakkal caves are located in the Wayanad district of Kerala.
  13. 13.
    Kerala Kalamandalam was established in
    Show answer and explanation
    Answer: C —
    1930
    Kerala Kalamandalam was established in 1930 by Vallathol Narayana Menon.
  14. 14.
    The Channar agitation is mainly for
    Show answer and explanation
    Answer: D —
    Right to wear upper body cloth
    The Channar agitation was a struggle for the right of lower-caste women to cover their upper bodies.
  15. 15.
    Who is the author of the drama 'Adukkalyilninnum Arangathekku ' ?
    Show answer and explanation
    Answer: A —
    V T Bhattathiripad
    V. T. Bhattathiripad wrote the play 'Adukkalyilninnum Arangathekku' to highlight the plight of Namboodiri women.
  16. 16.
    Who was the editor of the literary journal 'Vivekodyam' which started publication in Kerala in 1904 ?
    Show answer and explanation
    Answer: D —
    Kumaran Asan
    Kumaran Asan was the editor of the journal 'Vivekodyam'.
  17. 17.
    The father of Library movement in Kerala
    Show answer and explanation
    Answer: B —
    Puthuvayil Narayana Panicker
    P. N. Panicker is known as the father of the Library movement in Kerala.
  18. 18.
    Who among the following is not related with the 'Abstention movement' ?
    Show answer and explanation
    Answer: A —
    A K Gopalan
    A. K. Gopalan was not associated with the Abstention movement (Nivarthana Prakshobham).
  19. 19.
    The Indian who won the Nobel Prize for peace in 2014
    Show answer and explanation
    Answer: C —
    Kailash Satyarthi
    Kailash Satyarthi won the Nobel Peace Prize in 2014 along with Malala Yousafzai.
  20. 20.
    The Right to Information Act came into force in ____
    Show answer and explanation
    Answer: B —
    12 October 2005
    The RTI Act came into full force on 12 October 2005.
  21. 21.
    Which measure of location will be suitable to compare heights of students in two classes?
    Show answer and explanation
    Answer: A —
    Mean
    The arithmetic mean is the most suitable measure for comparing central tendencies of continuous data like height.
  22. 22.
    The geometric mean of 2, 4, 16 and 32 is
    Show answer and explanation
    Answer: C —
    8
    Geometric Mean = (2×4×16×32)1/4=(4096)1/4=8(2 \times 4 \times 16 \times 32)^{1/4} = (4096)^{1/4} = 8.
  23. 23.
    The strength of seven colleges in a city are 385,1748,1343,1935,786,2874 and 2108. Then the median strength is
    Show answer and explanation
    Answer: B —
    1748
    Arranging in ascending order: 385, 786, 1343, 1748, 1935, 2108, 2874. The middle value is 1748.
  24. 24.
    The mean and median of 100 items are 50 and 52 respectively. The value of the largest item is 100. It was later found that it is actually 110. Therefore, the true mean is ___ and the true median is _____ .
    Show answer and explanation
    Answer: A —
    50.1, 52
    New sum = (100×50)−100+110=5010(100 \times 50) - 100 + 110 = 5010. New mean = 5010/100=50.15010 / 100 = 50.1. Median remains unchanged as the change is in the extreme value.
  25. 25.
    10 is the mean of a set of 7 observations and 5 is the mean of a set of 3 observations. The mean of a combined set is given by
    Show answer and explanation
    Answer: C —
    8.5
    Combined Mean = (7×10)+(3×5)7+3=70+1510=8.5\frac{(7 \times 10) + (3 \times 5)}{7 + 3} = \frac{70 + 15}{10} = 8.5.
  26. 26.
    A distribution with more than two modes is called
    Show answer and explanation
    Answer: C —
    multimodal
    A distribution with more than two modes is defined as multimodal.
  27. 27.
    The algebraic sum of the deviations of a set of n values from their arithmetic mean is
    Show answer and explanation
    Answer: B —
    0
    By definition, ∑(xi−xˉ)=0\sum (x_i - \bar{x}) = 0.
  28. 28.
    When xix_i and yiy_i are two variables (i=1,2,...,n) with geometric means G1G_1 and G2G_2 respectively then the geometric mean of xiyi\frac{x_i}{y_i} is
    Show answer and explanation
    Answer: A —
    G1G2\frac{G_1}{G_2}
    The geometric mean of a ratio of two variables is the ratio of their geometric means.
  29. 29.
    The mean of the distribution, in which the value of x are 1,2,...,n, the frequency of each being unity is
    Show answer and explanation
    Answer: C —
    n+12\frac{n+1}{2}
    Mean = ∑i=1nin=n(n+1)/2n=n+12\frac{\sum_{i=1}^{n} i}{n} = \frac{n(n+1)/2}{n} = \frac{n+1}{2}.
  30. 30.
    The mean of 20 observations is 15. On checking it was found that two observations were wrongly copied as 3 and 6. If wrong observations are replaced by correct values 8 and 4, then the correct mean is
    Show answer and explanation
    Answer: A —
    15.15
    Correct sum = (20×15)−(3+6)+(8+4)=300−9+12=303(20 \times 15) - (3 + 6) + (8 + 4) = 300 - 9 + 12 = 303. Correct mean = 303/20=15.15303 / 20 = 15.15.
  31. 31.
    Sum of absolute deviations about median is
    Show answer and explanation
    Answer: A —
    least
    The sum of absolute deviations ∑∣xi−M∣\sum |x_i - M| is minimized when M is the median.
  32. 32.
    If each of a set of observations of a variable is multiplied by a constant (non-zero) value, the variance of the resultant variable
    Show answer and explanation
    Answer: B —
    increases
    If Y=cXY = cX, then Var(Y)=c2Var(X)Var(Y) = c^2 Var(X). If c>1c > 1, variance increases.
  33. 33.
    The standard deviation of a distribution is 5. The value of the fourth central moment μ4\mu_4 in order that the distribution be mesokurtic should be
    Show answer and explanation
    Answer: C —
    equal to 1875
    For a mesokurtic distribution, β2=μ4σ4=3\beta_2 = \frac{\mu_4}{\sigma^4} = 3. Given σ=5\sigma = 5, σ4=625\sigma^4 = 625. Thus μ4=3×625=1875\mu_4 = 3 \times 625 = 1875.
  34. 34.
    In a frequency curve of scores the mode was found to be higher than the mean. This shows that the distribution is
    Show answer and explanation
    Answer: B —
    negatively skewed
    In a negatively skewed distribution, Mean < Median < Mode.
  35. 35.
    The probability of drawing any one spade card from a pack of cards is
    Show answer and explanation
    Answer: D —
    14\frac{1}{4}
    There are 13 spades in a deck of 52 cards. 13/52=1/413/52 = 1/4.
  36. 36.
    A coin is tossed three times in succession, the number of sample points in sample space is
    Show answer and explanation
    Answer: B —
    8
    For nn tosses, the sample space size is 2n2^n. For n=3n=3, 23=82^3 = 8.
  37. 37.
    A single letter is selected at random from the word 'probability'. The probability that it is a vowel is
    Show answer and explanation
    Answer: C —
    411\frac{4}{11}
    The word 'probability' has 11 letters. Vowels are o, a, i, i (4). Probability = 4/11.
  38. 38.
    A number is chosen at random among the first 120 natural numbers. The probability of the number chosen being a multiple of 5 or 15 is
    Show answer and explanation
    Answer: A —
    15\frac{1}{5}
    Multiples of 5 up to 120 are 120/5=24120/5 = 24. Multiples of 15 are 120/15=8120/15 = 8. Since all multiples of 15 are multiples of 5, the count is 24. Probability = 24/120=1/524/120 = 1/5.
  39. 39.
    If A and B are two independent events, the probability that both A and B occur is 1/81/8 and the probability that neither of them occurs is 3/83/8. The probability of the occurrence of A is
    Show answer and explanation
    Answer: A —
    12\frac{1}{2}
    P(A)P(B)=1/8P(A)P(B) = 1/8 and (1−P(A))(1−P(B))=3/8(1-P(A))(1-P(B)) = 3/8. Solving these yields P(A)=1/2P(A) = 1/2 or 1/41/4.
  40. 40.
    An urn contains 9 balls, two of which are red, three blue and four black. Three balls are drawn at random. The chance that they are of the same colour is
    Show answer and explanation
    Answer: A —
    584\frac{5}{84}
    Total ways = 9C3=84^9C_3 = 84. Ways to get 3 of same color = 3C3^3C_3 (blue) + 4C3^4C_3 (black) = 1+4=51 + 4 = 5. Probability = 5/845/84.
  41. 41.
    In the simultaneous tossing of two perfect coins, the probability of having atleast one head is
    Show answer and explanation
    Answer: C —
    34\frac{3}{4}
    Sample space: {HH, HT, TH, TT}. At least one head: {HH, HT, TH}. Probability = 3/4.
  42. 42.
    For two events E1,E2E_1, E_2 if P(E1)=1/2,P(E2)=1/3,P(E1∪E2)=2/3P(E_1) = 1/2, P(E_2) = 1/3, P(E_1 \cup E_2) = 2/3 then P(E1∩E2)P(E_1 \cap E_2) is equal to
    Show answer and explanation
    Answer: B —
    16\frac{1}{6}
    P(E1∪E2)=P(E1)+P(E2)−P(E1∩E2)⇒2/3=1/2+1/3−P(E1∩E2)⇒P(E1∩E2)=5/6−2/3=1/6P(E_1 \cup E_2) = P(E_1) + P(E_2) - P(E_1 \cap E_2) \Rightarrow 2/3 = 1/2 + 1/3 - P(E_1 \cap E_2) \Rightarrow P(E_1 \cap E_2) = 5/6 - 2/3 = 1/6.
  43. 43.
    If P(A/B)=1/4P(A/B) = 1/4 and P(B/A)=1/3P(B/A) = 1/3, then P(A)P(B)\frac{P(A)}{P(B)} is equal to
    Show answer and explanation
    Answer: A —
    34\frac{3}{4}
    P(A∩B)=P(A/B)P(B)=P(B/A)P(A)⇒(1/4)P(B)=(1/3)P(A)⇒P(A)/P(B)=(1/4)/(1/3)=3/4P(A \cap B) = P(A/B)P(B) = P(B/A)P(A) \Rightarrow (1/4)P(B) = (1/3)P(A) \Rightarrow P(A)/P(B) = (1/4)/(1/3) = 3/4.
  44. 44.
    If P1(x)P_1(x) and P2(x)P_2(x) be the marginal probability functions of two independent discrete random variables X and Y, then their joint probability function P(x,y)=P(x,y) =
    Show answer and explanation
    Answer: B —
    P1(x)P2(y)P_1(x)P_2(y)
    For independent random variables, the joint probability mass function is the product of marginal probability mass functions.
  45. 45.
    The function f(x)f(x) defined as f(x)={∣x∣if −1<x<10elsewheref(x) = \begin{cases} |x| & \text{if } -1 < x < 1 \\ 0 & \text{elsewhere} \end{cases} is a possible
    Show answer and explanation
    Answer: A —
    density function
    A function is a probability density function if ∫f(x)dx=1\int f(x) dx = 1. Here ∫−11∣x∣dx=2∫01xdx=2[x2/2]01=1\int_{-1}^{1} |x| dx = 2 \int_{0}^{1} x dx = 2[x^2/2]_0^1 = 1.
  46. 46.
    For two random variables X and Y, the relation E(XY)=E(X)E(Y)E(XY) = E(X)E(Y) holds good
    Show answer and explanation
    Answer: A —
    if X and Y are statistically independent.
    Independence of random variables is a sufficient condition for the expectation of their product to be the product of their expectations.
  47. 47.
    Var(2X±3)Var(2X \pm 3) if Var(X)=1Var(X)=1 is
    Show answer and explanation
    Answer: C —
    4
    Var(aX+b)=a2Var(X)Var(aX + b) = a^2 Var(X). Thus Var(2X±3)=22Var(X)=4(1)=4Var(2X \pm 3) = 2^2 Var(X) = 4(1) = 4.
  48. 48.
    E(X−k)2E(X-k)^2 is minimum when
    Show answer and explanation
    Answer: C —
    k=E(X)k = E(X)
    The mean squared error E(X−k)2E(X-k)^2 is minimized when kk is the expected value E(X)E(X).
  49. 49.
    The height of persons in a country is a random variable of the type
    Show answer and explanation
    Answer: A —
    continuous random variable
    Height is a measurement that can take any value within a range, making it a continuous random variable.
  50. 50.
    If X is a random variable, E(etX)E(e^{tX}) is known as
    Show answer and explanation
    Answer: B —
    moment generating function
    The moment generating function (MGF) of a random variable X is defined as MX(t)=E(etX)M_X(t) = E(e^{tX}).
  51. 51.
    The mean and variance of a binomial distribution are 8 and 4 respectively. Then P(X=1)P(X=1) is equal to
    Show answer and explanation
    Answer: D —
    1212\frac{1}{2^{12}}
    np=8,npq=4  ⟹  q=0.5,p=0.5,n=16np=8, npq=4 \implies q=0.5, p=0.5, n=16. P(X=1)=(161)(0.5)1(0.5)15=16×(0.5)16=24×2−16=2−12=1212P(X=1) = \binom{16}{1} (0.5)^1 (0.5)^{15} = 16 \times (0.5)^{16} = 2^4 \times 2^{-16} = 2^{-12} = \frac{1}{2^{12}}.
  52. 52.
    A probability distribution in which mean is equal to variance is
    Show answer and explanation
    Answer: D —
    Poisson
    For a Poisson distribution with parameter λ\lambda, both the mean and the variance are equal to λ\lambda.
  53. 53.
    An experiment succeeds twice as often as it fails. The chance that in the next six trials, there shall be atleast four successes is
    Show answer and explanation
    Answer: D —
    496729\frac{496}{729}
    p=2/3,q=1/3,n=6p=2/3, q=1/3, n=6. P(X≥4)=P(4)+P(5)+P(6)=(64)(2/3)4(1/3)2+(65)(2/3)5(1/3)1+(66)(2/3)6=15⋅16+6⋅32+64729=240+192+64729=496729P(X \ge 4) = P(4)+P(5)+P(6) = \binom{6}{4}(2/3)^4(1/3)^2 + \binom{6}{5}(2/3)^5(1/3)^1 + \binom{6}{6}(2/3)^6 = \frac{15 \cdot 16 + 6 \cdot 32 + 64}{729} = \frac{240+192+64}{729} = \frac{496}{729}.
  54. 54.
    The skewness in a binomial distribution will be zero, if
    Show answer and explanation
    Answer: D —
    p=12p = \frac{1}{2}
    A binomial distribution is symmetric (skewness = 0) when p=q=0.5p = q = 0.5.
  55. 55.
    The characteristic function of Poisson distribution is
    Show answer and explanation
    Answer: C —
    em(eit−1)e^{m(e^{it}-1)}
    The characteristic function of a Poisson distribution with mean mm is ϕ(t)=E(eitX)=em(eit−1)\phi(t) = E(e^{itX}) = e^{m(e^{it}-1)}.
  56. 56.
    The coefficient of variation of Poisson distribution with mean 4 is
    Show answer and explanation
    Answer: B —
    24\frac{2}{4}
    Mean λ=4\lambda=4, S.D. σ=λ=2\sigma = \sqrt{\lambda} = 2. CV=(σ/μ)×100=(2/4)×100=50%CV = (\sigma/\mu) \times 100 = (2/4) \times 100 = 50\%.
  57. 57.
    If X is a normal variate representing the income in Rs. per day with mean=50 and S.D=10. If the number of workers in a factory is 1200, then the number of workers having income more than Rs. 62.00 per day is (given ϕ(1.2)=0.3849\phi(1.2) = 0.3849 where Z is a standard normal variate)
    Show answer and explanation
    Answer: C —
    138
    Z=(62−50)/10=1.2Z = (62-50)/10 = 1.2. P(X>62)=P(Z>1.2)=0.5−0.3849=0.1151P(X > 62) = P(Z > 1.2) = 0.5 - 0.3849 = 0.1151. 1200×0.1151≈1381200 \times 0.1151 \approx 138.
  58. 58.
    If X∼Exp(5)X \sim Exp(5), then the probability density function of X is
    Show answer and explanation
    Answer: A —
    5e−5x,x>05e^{-5x}, x>0
    The PDF of an exponential distribution with rate parameter λ\lambda is f(x)=λe−λxf(x) = \lambda e^{-\lambda x}. Here λ=5\lambda=5.
  59. 59.
    The distribution for which mode does not exist is
    Show answer and explanation
    Answer: C —
    continuous rectangular distribution
    In a continuous uniform (rectangular) distribution, the density is constant over the interval, so no unique mode exists.
  60. 60.
    Assume that the height of students is distributed as N(μ,σ2)N(\mu, \sigma^2). Out of a large number of students, 5 percent are above 72 inches and 10 percent are below 60 inches. The mean and S.D. of the normal distribution are (given ϕ(z1)=0.45,z1=1.64,ϕ(z2)=0.4,z2=1.28\phi(z_1)=0.45, z_1=1.64, \phi(z_2)=0.4, z_2=1.28 where ϕ(z)=∫0zf(z)dz\phi(z)=\int_0^z f(z)dz)
    Show answer and explanation
    Answer: D —
    μ=65,Σ=4\mu=65, \Sigma=4
    72=μ+1.64σ72 = \mu + 1.64\sigma and 60=μ−1.28σ60 = \mu - 1.28\sigma. Solving these gives μ=65\mu=65 and σ=4\sigma=4.
  61. 61.
    A box contains 12 items out of which 4 are defective. A person selects 6 items from the box. The expected number of defective items out of his selected items is
    Show answer and explanation
    Answer: A —
    2
    This follows a hypergeometric distribution. E(X)=n×(K/N)=6×(4/12)=6×(1/3)=2E(X) = n \times (K/N) = 6 \times (4/12) = 6 \times (1/3) = 2.
  62. 62.
    If X is a normal variate with mean 20 and variance 64, the probability that X lies between 12 and 32 is (Given z : -1.0, 1.5; ϕ(z):0.3143,0.4332\phi(z): 0.3143, 0.4332)
    Show answer and explanation
    Answer: C —
    0.7475
    Z1=(12−20)/8=−1.0Z_1 = (12-20)/8 = -1.0, Z2=(32−20)/8=1.5Z_2 = (32-20)/8 = 1.5. P(−1<Z<1.5)=ϕ(1.0)+ϕ(1.5)=0.3143+0.4332=0.7475P(-1 < Z < 1.5) = \phi(1.0) + \phi(1.5) = 0.3143 + 0.4332 = 0.7475.
  63. 63.
    If Z is a standard normal variate, the proportion of items lying between z=-0.5 and z=-3.0 is
    Show answer and explanation
    Answer: C —
    0.3072
    P(−3<Z<−0.5)=P(0.5<Z<3)=P(Z<3)−P(Z<0.5)=0.4987−0.1915=0.3072P(-3 < Z < -0.5) = P(0.5 < Z < 3) = P(Z < 3) - P(Z < 0.5) = 0.4987 - 0.1915 = 0.3072.
  64. 64.
    Factorization theorem for sufficiency is known as
    Show answer and explanation
    Answer: D —
    Fisher-Neyman theorem
    The Fisher-Neyman factorization theorem provides a necessary and sufficient condition for a statistic to be sufficient.
  65. 65.
    If the expected value of an estimator is not equal to its parametric function τ(Θ)\tau(\Theta), it is said to be a
    Show answer and explanation
    Answer: B —
    biased estimator
    An estimator is biased if E(θ^)≠θE(\hat{\theta}) \neq \theta.
  66. 66.
    An estimator TnT_n of θ\theta is said to be more efficient than any other estimator Tn′T'_n of θ\theta if and only if
    Show answer and explanation
    Answer: D —
    All the above
    All three expressions equivalently state that TnT_n has a smaller variance than Tn′T'_n, making it more efficient.
  67. 67.
    If σ2\sigma^2 is the population variance and s2=1n∑i=1n(Xi−Xˉ)2s^2 = \frac{1}{n} \sum_{i=1}^n (X_i - \bar{X})^2 is the sample variance, then s2s^2 is an unbiased estimate of
    Show answer and explanation
    Answer: D —
    n−1nσ2\frac{n-1}{n} \sigma^2
    The sample variance with divisor nn is biased, and its expected value is n−1nσ2\frac{n-1}{n}\sigma^2.
  68. 68.
    The sample median is _______________ estimate for the mean of normal population.
    Show answer and explanation
    Answer: C —
    unbiased and consistent
    For a normal population, the sample median is both an unbiased and consistent estimator of the population mean.
  69. 69.
    If a sufficient estimator exists it is a function of the _______ estimator.
    Show answer and explanation
    Answer: C —
    maximum likelihood estimator
    By the Fisher-Neyman theorem and properties of sufficient statistics, any sufficient statistic is a function of the maximum likelihood estimator.
  70. 70.
    The credit of inventing the method of moments for estimating the parameter goes to
    Show answer and explanation
    Answer: D —
    Karl Pearson
    Karl Pearson introduced the method of moments for parameter estimation in 1894.
  71. 71.
    Cramer-Rao inequality with regard to the variance of an estimator provides
    Show answer and explanation
    Answer: B —
    lower bound on the variance
    The Cramér-Rao lower bound establishes a lower bound on the variance of any unbiased estimator.
  72. 72.
    If X1,X2,...,XnX_1, X_2, ..., X_n is a random sample from a population N(0,σ2)N(0, \sigma^2), the sufficient statistic for σ2\sigma^2 is
    Show answer and explanation
    Answer: B —
    ∑Xi2\sum X_i^2
    Using the factorization theorem, ∑Xi2\sum X_i^2 is sufficient for σ2\sigma^2 when mean is known to be zero.
  73. 73.
    Estimate and Estimator are
    Show answer and explanation
    Answer: C —
    different
    An estimator is a rule or formula (random variable), whereas an estimate is a specific numerical value calculated from sample data.
  74. 74.
    The idea of testing of hypothesis was first set forth by
    Show answer and explanation
    Answer: B —
    J.Neyman
    The formal theory of hypothesis testing was primarily developed and set forth by Jerzy Neyman and Egon Pearson.
  75. 75.
    A wrong decision about H0H_0 leads to
    Show answer and explanation
    Answer: B —
    two kinds of errors
    Hypothesis testing errors are classified into two types: Type I error and Type II error.
  76. 76.
    In terms of type II error β\beta and θ\theta, the true parameter, the function 1−β(θ)1-\beta(\theta) is called
    Show answer and explanation
    Answer: B —
    power function
    The function 1−β(θ)1 - \beta(\theta) representing the probability of rejecting the null hypothesis when it is false is the power function.
  77. 77.
    A population is distributed as N(μ,10.24)N(\mu, 10.24). A sample of 576 items has a mean 4.7. The value of the statistic Z to test H0:μ=5.2H_0: \mu = 5.2 is
    Show answer and explanation
    Answer: C —
    -3.75
    Z=4.7−5.210.24/576=−0.53.2/24=−0.50.1333=−3.75Z = \frac{4.7 - 5.2}{\sqrt{10.24}/\sqrt{576}} = \frac{-0.5}{3.2/24} = \frac{-0.5}{0.1333} = -3.75.
  78. 78.
    A sample of 12 specimen taken from a normal population is expected to have a mean 50 mg/cc. The sample has a mean 64 mg/cc with a variance of 25. To test H0:μ=50 vs. H1:μ≠50H_0: \mu = 50 \text{ vs. } H_1: \mu \neq 50, you will use
    Show answer and explanation
    Answer: D —
    t-test
    Since sample size is small (n<30n < 30) and population variance is unknown, Student's t-test is used.
  79. 79.
    Testing H0:μ=1500H_0: \mu = 1500 against μ<1500\mu < 1500 leads to
    Show answer and explanation
    Answer: A —
    one-sided lower tailed test
    The alternative hypothesis μ<1500\mu < 1500 defines a one-sided lower tailed test.
  80. 80.
    The mean difference between 9 paired observations is 15.0 and the standard deviation of differences is 5.0. The value of statistic t is
    Show answer and explanation
    Answer: B —
    9
    t=dˉSd/n=15.05.0/9=15.05.0/3=15×35=9t = \frac{\bar{d}}{S_d / \sqrt{n}} = \frac{15.0}{5.0 / \sqrt{9}} = \frac{15.0}{5.0 / 3} = \frac{15 \times 3}{5} = 9.
  81. 81.
    Range of statistic t is
    Show answer and explanation
    Answer: B —
    −∞-\infty to ∞\infty
    The Student's t-statistic can take any real value from −∞-\infty to ∞\infty.
  82. 82.
    Given the following eight sample values -4, -3, -3, 0, 3, 3, 4, 4 the value of student's t-statistic to test H0:μ=0H_0: \mu = 0 is
    Show answer and explanation
    Answer: D —
    0.41
    Calculating sample mean, standard deviation, and t-value for n=8n=8 gives approximately 0.41.
  83. 83.
    In a contingency table, the expected frequencies are computed under
    Show answer and explanation
    Answer: A —
    null hypothesis H0H_0
    Expected frequencies in chi-square tests of independence are computed assuming the null hypothesis of independence is true.
  84. 84.
    The term regression was introduced by
    Show answer and explanation
    Answer: B —
    Sir Francis Galton
    Sir Francis Galton introduced the concept and term 'regression' in his studies of inheritance.
  85. 85.
    If byxb_{yx} and bxyb_{xy} are two regression coefficients they have
    Show answer and explanation
    Answer: A —
    same sign
    Both regression coefficients must always have the same sign, which is identical to the sign of the correlation coefficient rr.
  86. 86.
    The lines of regression intersect at the point
    Show answer and explanation
    Answer: D —
    (xˉ,yˉ)(\bar{x}, \bar{y})
    The two regression lines always intersect at the point of means (xˉ,yˉ)(\bar{x}, \bar{y}).
  87. 87.
    If a constant 50 is subtracted from each of the value of X and Y, the regression coefficient is
    Show answer and explanation
    Answer: D —
    not changed
    Regression coefficients are independent of change of origin (shifting/subtracting constants).
  88. 88.
    If r is the simple correlation coefficient, the quantity r2r^2 is known as
    Show answer and explanation
    Answer: A —
    coefficient of determination
    The square of the correlation coefficient (r2r^2) is called the coefficient of determination.
  89. 89.
    The range of simple correlation coefficient is
    Show answer and explanation
    Answer: D —
    -1 to 1
    The simple correlation coefficient rr always lies between -1 and 1 inclusive.
  90. 90.
    The hypothesis for a specific known value of r can be tested by
    Show answer and explanation
    Answer: B —
    Z-test
    Fisher's Z-transformation is commonly used to test hypotheses concerning the population correlation coefficient.
  91. 91.
    A measure of linear association of a variable with a number of other variables is known as
    Show answer and explanation
    Answer: D —
    multiple correlation
    Multiple correlation measures the association between one variable and a set of other predictor variables.
  92. 92.
    Given the regression lines X+2Y−5=0X+2Y-5=0, 2X+3Y−8=02X+3Y-8=0 and Var(X)=12\text{Var}(X)=12, the value of Var(Y)\text{Var}(Y) is
    Show answer and explanation
    Answer: D —
    4
    Solving the system of equations and using the properties of regression coefficients yields Var(Y)=4\text{Var}(Y) = 4.
  93. 93.
    Given r12=0.6r_{12} = 0.6, r13=0.5r_{13} = 0.5 and r23=0.8r_{23} = 0.8, the value of r12.3r_{12.3} is
    Show answer and explanation
    Answer: C —
    0.38
    Using the partial correlation formula r12.3=r12−r13r23(1−r132)(1−r232)≈0.38r_{12.3} = \frac{r_{12} - r_{13}r_{23}}{\sqrt{(1-r_{13}^2)(1-r_{23}^2)}} \approx 0.38.
  94. 94.
    The sales of a departmental store on Dushera and Diwali are associated with the component of a time series
    Show answer and explanation
    Answer: C —
    seasonal variation
    Festival sales like Dushera and Diwali occur at specific times annually, representing seasonal variations.
  95. 95.
    Which index satisfies factor reversal test?
    Show answer and explanation
    Answer: D —
    Fisher's ideal index
    Fisher's Ideal Index is known as the ideal index because it satisfies both the time reversal test and the factor reversal test.
  96. 96.
    Control chart consists of
    Show answer and explanation
    Answer: A —
    three control lines
    A control chart consists of three lines: Upper Control Limit (UCL), Central Line (CL), and Lower Control Limit (LCL).
  97. 97.
    Replication in an experiment means
    Show answer and explanation
    Answer: B —
    the number of times a treatment occurs in an experiment
    Replication refers to the repetition of each treatment in an experiment.
  98. 98.
    Local control in experimental designs is meant to
    Show answer and explanation
    Answer: D —
    all the above
    Local control helps in forming homogeneous blocks, reducing experimental error, and increasing overall design efficiency.
  99. 99.
    The number of possible samples of size n out of N population units without replacement is
    Show answer and explanation
    Answer: A —
    (Nn)\binom{N}{n}
    The number of distinct possible samples of size n drawn without replacement from N population units is given by combinations (Nn)\binom{N}{n}.
  100. 100.
    Moving average method of fitting trend in a time series data removes the effect of
    Show answer and explanation
    Answer: D —
    short-term movements
    The moving average method smoothens out fluctuations by filtering out short-term movements and irregular variations.

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