ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 72 - 77 of 165

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Question number: 72

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

Essay Question▾

Describe in Detail

In a ticket counter, at some point of time the sequence of males (M) and females (F) was found as

MMFMFFFMFMMFFFFMFMMMM

Use runs test to examine if the sequence is random (5 % critical value of the number r of runs with n 1 = 11, n 2 = 10 is 6).

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: 73

» Statistical Methods » Measures of Location

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X have the probability density function

Find the mean, geometric mean and harmonic mean.

Explanation

Then mean is

The geometric mean is

The geometric mean is

The harmonic mean is

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Question number: 74

» Probability » Tchebycheffs Inequality

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let X be a positive valued random variable. Prove that

Hence deduce the Chebychev’s inequality.

Explanation

The expectation of X is define as

For any x ≥ r

This implies that

Hence, any function of X, assume g (x) the Chebychev’s inequality is

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Question number: 75

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let Y 1 denote the first order statistic in a random sample of size n from a distribution that has the pdf

Obtain the distribution of Z n =n (Y 1 -θ).

Explanation

To find the distribution of order statistic, the pdf is

Here denote the first order statistic that is

The cdf of x is

The pdf of Y 1 is

Then, the dis

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Question number: 76

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

Appeared in Year: 2010

Essay Question▾

Describe in Detail

If f (x) =1/x 2, find the divided differences f (a, b) and f (a, b, c).

Explanation

we can write the Newton’s divided difference formulas as

First find f (b, c)

Then, from (1) and (2)

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Question number: 77

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2015

Essay Question▾

Describe in Detail

If X follows binomial b (n 1, p 1) distribution and Y follows binomial b (n 2, p 2), provide an appropriate test at level α for H 0: p 1 =p 2 against H 1: p 1 > p 2.

Explanation

The hypothesis is equivalent to testing the null hypothesis that p 1 −p 2 = 0 against the alternative is p 1 -p 2 > 0. The statistic on which we base our decision is the random variable . Suppose the samples of sizes n 1 and n 2 are selected from binomial populations are independent.

For large sample size, the estimator was approximately

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