# 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

### 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

### 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

### 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

### 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 | 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

### 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

### 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) …