ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 115  119 of 165
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Question number: 115
» Statistical Methods » NonParametric Test » Wilcoxon
Appeared in Year: 2012
Describe in Detail
Ten shortdistance runners were put to a rigorous training for two months. Times taken by them to clear 100 metres before and after the training were as follows:
Sl. no. of runner  1  2  3  4  5  6  7  8  9  10 
Time (in sec) before training  10.6  10.9  10.1  10.5  11.0  11.2  10.7  10.2  10.9  10.6 
Time (in sec) after training  10.1  10.7  9.9  10.0  11.1  10.9  10.6  10.3  10.5  10.8 
Use Wilcoxon’s paired sample signed rank test to examine at 1 % level if the training was at all effective. (The critical value of Wilcoxon’s statistic at 1 % level of significance for n = 10 is 5)
Explanation
In Wilcoxon’s paired sample signed rank test, the null hypothesis that we are sampling two continuous symmetric populations with for the pairedsample case, we rank the differences of the paired observations without regard to sign and proceed as in the singlesample case
Let and represent the median
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.
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
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
Putting the value of c
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 
2  19  18  1.5   
5 