ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 25 - 30 of 165

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Question number: 25

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2015

Essay Question▾

Describe in Detail

Let (X, Y) be distributed as bivariate normal BVN (3,1, 16,25,3/5). 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 number: 26

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2009

Essay Question▾

Describe in Detail

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

H 0: P = 0.05 against H 1: P < 0.05

Here n = 300, numbers of defectives is 10 and

The estimated value of P is

The null hypothesis can be tested b

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Question number: 27

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2010

Essay Question▾

Describe in Detail

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 H 0

The test criteri

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Question number: 28

» Statistical Methods » Measures of Location

Appeared in Year: 2011

Essay Question▾

Describe in Detail

Let Z be a random variable with p. d. f. f (z). Let z α be its upper α th quantile. Show that if X is

a random variable with p. d. f. then σz α +µ is the upper α th quantile of X.

Explanation

Let Z be a random variable with p. d. f. f (z). Given that the quantile of z is defined as

X is a random variable with p. d. f. , then quantile is

Assume

Then the limit is

Lower limit is - and upper limit is

If z= then the integral is same for gi

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Question number: 29

» Probability » Tchebycheffs Inequality

Appeared in Year: 2014

Essay Question▾

Describe in Detail

Show that for 40,000 throws of a balanced coin, the probability is at least 0·99 that the proportion of heads will fall between 0·475 and 0·525.

Explanation

For balanced coin the probability is p = 0.5. For Bernoulli trails where n = 40,000, the mean and standard deviation is

Using Chebyshev’s inequality,

The question says that the probability is at least 0.99 that is

So, the number of heads comes between

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Question number: 30

» Numerical Analysis » Interpolation Formulae » Lagrange

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Use Simpson’s one-third rule to estimate approximately the area of the cross section of a river 80 feet wide, the depth d (in feet) at a distance x from one bank being given by the following table. :

x

0

10

20

30

40

50

60

70

80

d

0

4

7

9

12

15

14

8

3

Explanation

T he one-third rule of the integrand using Simpson’s rule is

The area of the cross section of a river 80 feet wide is

Here n = 8, b = 80, a = 0, h= (b-a) /n = 10

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