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▾

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.… (93 more words) …

Question number: 35

» Statistical Methods » Measures of Location

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let X have the probability density function

Equation

Find the mean, geometric mean and harmonic mean.

Explanation

Then mean is

Equation

Equation

Equation

Equation

The geometric mean is

Equation

Equation

Equation

Equation

The geometric mean is

Equation

The harmonic mean is

Equation

Equation

Equation

Equation

Question number: 36

» 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 Equation. Suppose the samples of sizes n 1 and n 2… (68 more words) …

Question number: 37

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Given the following correlation matrix of order 3 x 3

Equation

Calculate (i) r 12.3 (ii) r 1.23

Explanation

In general, the correlation matrix is in these notations

Equation

(i)

Equation

Equation

Equation

Equation

(ii)

Equation

Equation

Equation

Question number: 38

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2012

Essay Question▾

Describe in Detail

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 Equation with different sample size n 1, n 2, …, n k. The test of null hypothesis is that the means of k normal population is same and the alternative hypothesis is any two mean are not same.

Equation Vs… (75 more words) …

Question number: 39

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

Essay Question▾

Describe in Detail

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

Equation

Obtain the estimated linear regression of X on Y.

Explanation

Let the linear equation is

Equation

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

Equation

To differential this, we get the estimate of Equation and Equation

Equation

Equation

The given… (24 more words) …

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