# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 19 - 24 of 165

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## Question number: 19

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Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Let F n (x) be the distribution function define by

Is the lim F n (x) a distribution function? If not, why?

### Explanation

The function F n (x) is a distribution function if

By the definition , but here this is no

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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

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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 parame

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## Question number: 22

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Appeared in Year: 2013

Essay Question▾

### Describe in Detail

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 res

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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

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