# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 157 - 162 of 165

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## Question number: 157

» Statistical Methods » Tests of Significance » F-Test

Appeared in Year: 2014

### 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

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## Question number: 158

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

Appeared in Year: 2009

### Describe in Detail

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

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## Question number: 159

» Statistical Methods » Tests of Significance » Chi-Square

Appeared in Year: 2009

### Describe in Detail

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

### Explanation

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## Question number: 160

» Probability » Laws of Total and Compound Probability

Appeared in Year: 2011

### Describe in Detail

Verify the following identities:

(i)

(ii)

### Explanation

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## Question number: 161

» Numerical Analysis » Interpolation Formulae » Newton-Gregory

Appeared in Year: 2010

### Describe in Detail

Estimate U _{2} from the following table:

x | 1 | 2 | 3 | 4 | 5 |

U | 7 | - | 13 | 21 | 37 |

### Explanation

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## Question number: 162

» Probability » Distribution Function » Standard Probability Distributions

Appeared in Year: 2011

### Describe in Detail

Show that is a probability density function for an appropriate value of a. Upto what order do the moments of this p. d. f. exist?

### Explanation

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