Statistical Methods (ISS Statistics Paper I (Old Subjective Pattern)): Questions 34 - 39 of 72

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Question number: 34

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

Essay Question▾

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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.… (93 more words) …

Question number: 35

» Statistical Methods » Measures of Location

Appeared in Year: 2015

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Let X have the probability density function

f(x)={(α+1)xα;0<x<1,α>10;otherwise

Find the mean, geometric mean and harmonic mean.

Explanation

Then mean is

E(X)=01xf(x)dx

=(α+1)01xα+1dx

=(α+1)[xα+2α+2]01… (159 more words) …

Question number: 36

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2015

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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 P^1P^2. Suppose the samples of… (142 more words) …

Question number: 37

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2014

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Given the following correlation matrix of order 3 x 3

R=[10.57080.673510.44871]

Calculate (i) r 12.3 (ii) r 1.23

Explanation

In general, the correlation matrix is in these notations

R=[1r12r13r211r23r31r321]

(i)

r12.3=r12r13r23(1r132)(1r… (64 more words) …

Question number: 38

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2012

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Indicate how you would test the hypothesis that the means of k independent normal populations are identical, clearly mentioning the null and the alternative hypotheses, the assumptions made, the test statistic used, and the critical region.

Explanation

Let there are k independent normal population N(μ1,σ12),N(μ2,σ22),,N(μk,σk2) with different sample size n 1, n 2, …, n… (311 more words) …

Question number: 39

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

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From a bivariate data set of 4995 observations, the following quantities have been calculated:

x=2353,x2=9508,y=1400,y2=70802,xy=8805

Obtain the estimated linear regression of X on Y.

Explanation

Let the linear equation is

X=β0+β1Y+ε

To solve this equation by least square method. In this approach, the residual sum of squares is minimized by partially differentiating with respect to β0 and β1.

ε2=… (139 more words) …

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