# Statistical Methods (ISS (Statistical Services) 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

### 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: 35

» Statistical Methods » Measures of Location

Appeared in Year: 2015

### 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: 36

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2015

### 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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## Question number: 37

» Statistical Methods » Correlation Coefficient » Partial Correlation

Appeared in Year: 2014

### Describe in Detail

Given the following correlation matrix of order 3 x 3

Calculate (i) r _{12.3} (ii) r _{1.23}

### Explanation

In general, the correlation matrix is in these notations

(i)

(ii)

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## Question number: 38

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2012

### 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 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.

Vs H _{1}: at least two mean are not equal

Under the assumptions that the

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## Question number: 39

» Statistical Methods » Regression » Linear

Appeared in Year: 2011

### Describe in Detail

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

Obtain the estimated linear regression of X on Y.

### Explanation

Let the linear equation is

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

To differential this, we get the estimate of and

The given value is putting in these e

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