ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 157 - 161 of 165

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Question number: 157

» Statistical Methods » Tests of Significance » F-Test

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Appeared in Year: 2014

Essay Question▾

Describe in Detail

Explain the procedure for testing the hypothesis of equality of variances of two independent normal populations when population means are unknown. Write down the sampling distribution of the statistic. A sample of size 10 is drawn from each of two uncorrelated normal populations. Sample means and variances are:

1 st population: mean = 7, variance = 26

2 nd population: mean = 4; variance = 10

Test at 5 % level of significance whether the first population has greater standard deviation than that of the second population. [Given F 0.05,9, 9 = 3·18]

Explanation

Let X 1, X 2, …, X n and Y 1, Y 2, …Y m are the samples taken from independent N (µ 1, σ 1 2) and N (µ 2, σ 2 2).

In this question the hypothesis for testing is

Let s 1 2 and s 2 2 be the estimates variances of σ 1 2 and σ 2 2 based on sample sizes n and m.

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Question number: 158

» Statistical Methods » Non-Parametric Test » Mann-Whitney

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Appeared in Year: 2009

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Given the following data:

x

0

1

3

f (x)

1

3

55

find a polynomial P (x) of degree 2 or less so that P (x) = f (x) at the tabulated values of x. Hence

approximate f (2).

Explanation

Let the a polynomial is P (X) = kx 2 +lx + m, where k, l, m are constants which is determine by using Lagrange’s interpolation polynomial because the x values is not equal interval.

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Question number: 159

» Statistical Methods » Tests of Significance » Chi-Square

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Appeared in Year: 2009

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Explain the method of testing normality by using chi-squared test.

Explanation

Let X is a random variable follows normal distribution with mean µ and variance σ 2. The testing of null hypothesis is that the population variance σ 2 equals a specified value against one of the usual alternatives σ 2 < , σ 2 > , or σ 2 . The appropriate statistic on which to base our d

… (137 more words) …

Question number: 160

» Probability » Laws of Total and Compound Probability

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Appeared in Year: 2011

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Verify the following identities:

(i)

(ii)

Explanation

Let A and B are two possible events in the sample space.

(i) Additive law of probability is

{Commutative property }

We know that

T

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Question number: 161

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

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Appeared in Year: 2010

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Estimate U 2 from the following table:

x

1

2

3

4

5

U x

7

-

13

21

37

Explanation

To find the missing value, we use binomial expansion method. Here 4 values are known, we would take fourth order finite difference zero. Thus,

Here for x = 1, U 0 =7, U 1 =? , U 2 =13, U 3 =21, U 4 =37

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