ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 116 - 121 of 165

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Question number: 116

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2013

Essay Question▾

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

… (65 more words) …

Question number: 117

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2011

Essay Question▾

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

… (186 more words) …

Question number: 118

» Probability » Standard Probability Distributions » Lognormal

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X follow log-normal with parameters µ and σ 2. Find the distribution of Y = aX b, a > 0, -∞ < b < ∞

Explanation

If X follow log-normal 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

… (207 more words) …

Question number: 119

» Numerical Analysis » Interpolation Formulae » Newton (Dividend Difference)

Appeared in Year: 2012

Essay Question▾

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 x-values 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

… (147 more words) …

Question number: 120

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2015

Essay Question▾

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

… (209 more words) …

Question number: 121

» Statistical Methods » Correlation Coefficient » Intraclass Correlation

Appeared in Year: 2012

Essay Question▾

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

… (208 more words) …

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