# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 18 - 22 of 164

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## Question 18

Appeared in Year: *2009*

### Describe in Detail

Essay▾wo drugs were given to two batches of 6 students. The numbers of days to get a complete cure are given below:

Durg A | 6 | 7 | 8 | 9 | 12 | 16 |

Durg B | 10 | 11 | 13 | 14 | 15 | 17 |

Using Mann-Whitney test decide whether the median days for cure by the two drugs are equal. (Table values of U - Statistic at 0·05 level are: U_{5,5} = 2, U_{5,6} = 3, and U_{6,6} = 5.)

### Explanation

Let the Durg A consider the population X and Durg B consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Mann-Whitney test, first consider the combined ordered sequence of the sample values is

Sample: 6 7 8 9 10 11 12 13 14 15 16 17

Population: X …

… (86 more words) …

## Question 19

Appeared in Year: *2010*

### Describe in Detail

Essay▾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 not equal to one. This says that F_{n} (x) is not a distribution function.

## Question 20

Appeared in Year: *2013*

### Describe in Detail

Essay▾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_{3} is

the parital correlation between X_{2} and X_{3} is

The multiple correlation coefficients ar…

… (53 more words) …

## Question 21

Appeared in Year: *2014*

### Describe in Detail

Essay▾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 parameter.

When we have t…

… (132 more words) …

## Question 22

Appeared in Year: *2013*

### Describe in Detail

Essay▾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

(ii) The generating function of Pr [X < n] is denoted by P (z_{< n})

The generating function is

(iii) The generating function of Pr [X …

… (6 more words) …