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

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Question 18

Appeared in Year: 2009

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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: U5,5 = 2, U5,6 = 3, and U6,6 = 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 &#8230;

… (86 more words) …

Question 19

Appeared in Year: 2010

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Essay▾

Let Fn (x) be the distribution function define by

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

Explanation

The function Fn (x) is a distribution function if

By the definition , but here this is not equal to one. This says that Fn (x) is not a distribution function.

Question 20

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Appeared in Year: 2013

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Essay▾

For a trivariate population, it is given that:

σ1 = 3, σ2 = 4, σ3 = 5, r12 = 0.7, r13 = 0.6, r23 = 0.4

Compute all partial and multiple correlation coefficients.

Explanation

Given that there are three variable X1 , X2 , X3 for a trivariate population. The partial correlation coefficient is between any two variable eliminating the third variable. So, the parital correlation between X1 and X2 is

the parital correlation between X1 and X3 is

the parital correlation between X2 and X3 is

The multiple correlation coefficients ar&#8230;

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Question 21

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Appeared in Year: 2014

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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 H0 and actual value of the parameter.

When we have t&#8230;

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Question 22

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Appeared in Year: 2013

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Essay▾

Let P (z) be the probability generating function of the random variable X whose probability distribution is Pr [X = n] = pn , 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] = pn . 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 &#8230;

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