Indian Statistical Institute Kolkata Associate Scientist Statistics Sample Paper Section II
Sample Questions on Statistics for Online Test Scientis ISI Kolkata
Note – For each of the questions there are four suggested answers, of which only one is correct. You will score
4 marks for each correctly answered question,
0 mark for each incorrectly answered questions, and
1 mark for each unattempted question.
Suppose 50 men out of 10,000 and 25 women out of 10,000 are colour blind in a large population, where males and females are in equal proportion. If a colour blind person is chosen at random, the probability of the person being male is
(a) 1/3
(b) 2/3
(c) 3/4
(d) 4/5
Let X be a discrete random variable that takes values 4,5 and 6 with probabilities 0.2, 0.3 and 0.5, respectively. Then the expected value |X-5| is
(a) 0.7
(b) 0.3
(c) -0.3
(d) 0
A student tosses an unbiased coin 28 times. Let Y be a random variable denoting the number of heads in first n tosses whereas Z denotes the number of heads in last n tosses. What would be the value of n so that the correlation coefficient between Y and Z is 0.6?
(a) 7
(b) 10
(c) 14
(d) 20
A polling agency has decided to increase the size of its random sample of voters from about 2000 people to about 5000 people. The effect of this increase in sample size is to
(a) reduce the bias of the estimate
(b) increase the standard error of the estimate
(c) reduce the variability of the estimate
(d) increase the width of the confidence interval for the parameter
In a two-way classified model (without interaction) with 3 blocks and 3 treatements and a single observation per cell, one observation is accidentally lost. Then one can say with certainty that
(a) difference of effects of at least one pair of treatments will become non-estimable
(b) difference of effects of at least one pair of blocks will become non-estimable
(c) at least one estimable parameter will become non-estimable
(d) no estimable parameter will become non-estimable
After fitting a linear regression of Y on X, a statistician plots the residuals against the values of X. It is seen that with increase in values o fX, the values of residuals become more scattered. What does this indicate?
(a) presence of multicollinearity
(b) presence of heteroskedasticity
(c) autocorrelated errors
(d) measurement error of y variable
Hourly measurements of temperature are recorded at a weather station over a period of 10 years. Let X1, ……,X168 be the hourly temperature during the period 1st to 7th February, averaged over 10 years (e.g. X1 is the average of 10 temperature measureemnts taken in the first hour of 1st February of the different years). Then the time series X1,——X168 is likely to have
(a) a dominant trend component
(b) a dominant seasonal component
(c) a dominant random component
(d) no dominant component
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