ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 116  121 of 165
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Question number: 116
» Statistical Methods » NonParametric Test » Run
Appeared in Year: 2013
Describe in Detail
Describe the run test for randomness. For the sequence of outcomes of 14 tosses of a coin,
HTTHHHTHTTHHTH, .
test whether the outcomes are in random order. (Given the lower and upper critical values R _{L} = 3,
R _{u } = 12 at 0.05 significance level. )
Explanation
Suppose a sample size n contains n _{1} symbols of one type and n _{2} symbols of the other type. The null hypothesis is the symbols occur in random order, the alternative is the symbols occur in a set pattern. The lower and upper critical value is obtained from tables. If the observed number of runs in a sample lies in between these critical values, t
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Question number: 117
» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)
Appeared in Year: 2011
Describe in Detail
Use Simpson’s rule with five ordinates to compute an approximation to π with the help of the integration of the function (1 + x ^{2}) ^{1} from 0 to 1.
Explanation
T he rule of the integrand using Simpson’s rule for five ordinates is
where , n = 5
h= (1  0) /5 = 1/5
We divide the range 0 to 1 in five equal part i. e.
Use Simpson’s rule
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Question number: 118
» Probability » Standard Probability Distributions » Lognormal
Appeared in Year: 2015
Describe in Detail
Let X follow lognormal with parameters µ and σ ^{2}. Find the distribution of Y = aX ^{b}, a > 0, ∞ < b < ∞
Explanation
If X follow lognormal with parameters µ and σ ^{2}, then Z = logX follow normal distribution.
First find the cdf of Y
Let
The upper limit is c= , lower limit is
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Question number: 119
» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)
Appeared in Year: 2012
Describe in Detail
An unknown function u _{x} has been tabulated below for some selected values of x. Use Newton’s divided difference formula on these to find an approximate value of u _{3}:
x  0  2  5  10 
u _{x}  3  19  73  223 
Explanation
The Newton’s divided difference formula is used when the xvalues not equally spaced. The Newton’s formula of divided difference for estimating u _{x} corresponding to x is
where , , …
x  y 



0  3  8  2  0.05 
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Question number: 120
» Statistical Methods » Correlation Coefficient » Multiple Correlation
Appeared in Year: 2015
Describe in Detail
With 3 variables X _{1}, X _{2} and X _{3}, it is given that r _{13} =0.71, R _{1.23} =0.78. Find r _{12.3}.
Explanation
We know that
The relationship between the partial and multiple correlations is
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Question number: 121
» Statistical Methods » Correlation Coefficient » Intraclass Correlation
Appeared in Year: 2012
Describe in Detail
For a set of 10 pairs of observations (x _{i}, y _{j}), i = 1 (1) 10, the following calculations are available
Examine at 5 % level of significance if the two variables arc uncorrelated in the population.
Explanation
First, we calculate the sample correlation coefficient r
for i = 1 to 10
Putting the value in the formula for n = 10
The test hypothesis is
The test statistic is
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