# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 20 - 24 of 165

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## Question number: 20

» Statistical Methods » Correlation Coefficient » Multiple Correlation

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

For a trivariate population, it is given that:

σ 1 =3, σ 2 =4, σ 3 =5, r 12 =0.7, r 13 =0.6, r 23 =0.4

Compute all partial and multiple correlation coefficients.

### Explanation

Given that there are three variable X 1, X 2, X 3 for a trivariate population. The partial correlation coefficient is between any two variable eliminating the third variable. So, the parital correlation between X 1 and X 2 is

the parital correlation between X 1 and X

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## Question number: 21

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Appeared in Year: 2014

Essay Question▾

### Describe in Detail

Define power of a test and discuss its role in selecting the best test. Describe a test procedure for testing equality of means of two independent normal populations, when standard deviations are equal but unknown for small samples.

### Explanation

Power of a test: The power function is the probability of rejection the null hypothesis when the alternative hypothesis is true. In statistical terms,

The quantity 1-β is called the power of the test. So, the power of the test is depends upon the difference between the parameter values specified in H 0 and actual value of the pa

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## Question number: 22

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Appeared in Year: 2013

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Let P (z) be the probability generating function of the random variable X whose probability distribution is Pr [X = n] = p n, n = 0, I, 2, …… Find the generating function of (i) Pr [X > n],

(ii) Pr [X < n] and (iii) Pr [X = 2n].

### Explanation

Let P (z) be the probability generating function of the random variable X whose probability distribution is Pr [X = n] = p n. Then

(i) The generating function of Pr [X > n] is denoted by P (z > n)

The generating function is

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## Question number: 23

» Statistical Methods » Correlation Coefficient » Multiple Correlation

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Appeared in Year: 2012

Essay Question▾

### Describe in Detail

Define partial correlation coefficient r 12.3 between x 1 and x 2 eliminating from each the effect of x 3. Derive the expression for r 12.3 and comment on its usefulness in multivariate data analysis.

### Explanation

Partial correlation coefficient defined as a association between any two variables out of a set of eliminating the other variable. Consider three variables X 1, X 2 and X 3. Now we want to find out the partial correlation coefficient r 12.3 between X 1 and X 2 eliminating the linear effect of X 3 on X 1 and X 2. In this situation, define two resid

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## Question number: 24

» Statistical Methods » Non-Parametric Test » Wilcoxon

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Appeared in Year: 2009

Essay Question▾

### Describe in Detail

Ten experts have given scores of effectiveness on two teams A and B as given below.

 Expert Score on A Score on B 1 7 9 2 4 5 3 8 8 4 9 8 5 3 6 6 6 10 7 8 9 8 10 8 9 9 4 10 5 9

Are the distribution of scores for group A above that of group B?

### Explanation

Let n 1 be the number of scores of effectiveness on team A with median score m 1, and n 2 the number of scores of effectiveness on team B with median score m 2. Then the hypothesis is that the median score of the two teams are same against the alternative that they are not same.

For this first arrange the observations of the combi

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