# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 67 - 71 of 164

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## Question 67

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Appeared in Year: 2014

### Describe in Detail

Essay▾

Let X follow a binomial distribution B (n, P) . Explain the test procedure for

H0: P = P0 against H1: P > P0

when the sample size is (i) small, and (ii) large. It is desired to use sample proportion p as an estimator of the population proportion P, with probability 0·95 or higher, that p is within 0·05 of P. How large should sample size (n) be?

### Explanation

Let X follow a binomial distribution B (n, P) with mean nP and variance nP (1-P) . In testing the hypothesis

H0: P = P0 against H1: P > P0

The null hypothesis can be tested by z-test for assuming the sample size n is large (Central limit theorem) . For binomial distribution, the test statistic is

The test criteria is reject H0 if z-statistic is greate&#8230;

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## Question 68

Appeared in Year: 2015

### Describe in Detail

Essay▾

Compute the value of by Simpson՚s rd rule. Given that ln 4.0 = 1.39, ln 4.2 = 1.43, ln 4.4 = 1.48, ln 4.6 = 1.53, ln 4.8 = 1.57, ln 5.0 = 1.61, ln 5.2 = 1.65

### Explanation

So, the seven ordinates of the integrand using Simpson՚s rule is

Here,

Using Simpson՚s rule is

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## Question 69

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Appeared in Year: 2014

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Essay▾

Given the following values of the function y = f (x) ; evaluate f (4) and also find x for which f (x) = 25.

f (1) = 10, f (2) = 15, f (3) = 42.

### Explanation

Given that y = f (x) , So

x 1 2 3 4

y 10 15 42?

To find the missing value, we use binomial expansion method. Here 3 values are known, we would take third order finite difference zero. Thus,

Second question is that if we have given that value of y = f (x) = 25, then find x using Lagrange՚s inverse interpolation method

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## Question 70

Standard Probability Distributions

Appeared in Year: 2010

### Describe in Detail

Essay▾

Let (X, Y) be jointly distributed with p. d. f.

Find marginal probability density function of X and Y.

### Explanation

The marginal probability density function of X is

The range is 0 < x < 1

The marginal probability density function of Y is

The range is 0 < y < 1

## Question 71

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Appeared in Year: 2010

### Describe in Detail

Essay▾

The observed-values of a function are respectively 168,120, 72 and 63 at the four positions 3,7, 9 and 10 of the independent variable. What is the best estimate you can give for the value of the function at the position 6 of the independent variable?

### Explanation

Using Lagrange՚s formula

Given that a = 3, b = 7, c = 9, d = 10 and f (a) = 168, f (b) = 120, f (c) = 72, f (d) = 63

Find x = 6, the values of f (x) = ?

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