ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 23 - 27 of 164

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Question 23

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Appeared in Year: 2012

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Essay▾

Define partial correlation coefficient r12.3 between x1 and x2 eliminating from each the effect of x3 . Derive the expression for r12.3 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 X1 , X2 and X3 . Now we want to find out the partial correlation coefficient r12.3 between X1 and X2 eliminating the linear effect of X3 on X1 and X2 . In this situation, define two residual var&#8230;

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Question 24

Appeared in Year: 2009

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Essay▾

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 n1 be the number of scores of effectiveness on team A with median score m1 , and n2 the number of scores of effectiveness on team B with median score m2 . 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 combined samples (n1 + n2)&#8230;

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Question 25

Bivariate Normal Distribution

Appeared in Year: 2015

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Essay▾

Let (X, Y) be distributed as bivariate normal BVN (3, 1,16, 25, ) . Calculate P (4 < Y < 11.84|X = 7)

Explanation

We had known that the conditional distribution of Y given X has mean and variance .

Using conditional mean and variance ‎

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Question 26

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Appeared in Year: 2009

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Essay▾

A manufacturer of alkaline batteries expects that only 5 % of his products are defective. A random sample of 300 batteries contained 10 defectives. Can we conclude the proportion of defectives in the entire lot is less than 0·5 at 5 % level of significance?

Explanation

A random sample of 300 batteries contained 10 defectives. A manufacturer of alkaline batteries expects that only 5 % of his products are defective that is testing of hypothesis is

H0: P = 0.05 against H1: P < 0.05

Here n = 300, numbers of defectives is 10 and

The estimated value of P is

The null hypothesis can be tested by z-test for assuming the sampl&#8230;

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Question 27

Appeared in Year: 2010

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Essay▾

You are working as a purchase manager for a company. The following information has been supplied to you by two manufacturers of electric bulbs.

 Company A Company B Mean life 1300 1288 Standard deviation 82 93 Sample size 100 100

Which brand of bulbs are you going to purchase if you desire to take a risk of 5 % ?

Explanation

Here the sample size is n = 100

The standard deviation and mean of two samples is different. The null hypothesis is the mean life of bulb of company A is equal to the mean life of bulb of company B and alternative its differ.

The test statistic is

Under H0

The test criteria is reject H0 if , otherwise accept it

Here

The tabulated value of t-test is

The &#8230;

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