# ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 7 - 10 of 165

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## Question number: 7

» Statistical Methods » Non-Parametric Test » Wald-Wolfowitz

Appeared in Year: 2011

### Describe in Detail

Explain the Wald-Wolfowitz run test for randomness in a sequence of two types of symbols. Find E _{Ho} (R) where R denotes the number of runs of elements of one kind.

### Explanation

Suppose we have two sample x _{1}, x _{2}, …x _{n} and y _{1}, y _{2}, …, y _{m} and we wish to test that either both sample come from same population or not. We can use Wald-Wolfowitz run test for randomness.

First we arrange n x’s and m y’s in descending order of size (n + m). Then we consider the array of x’s and y’s and count the number of runs (R). A run is a se

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## Question number: 8

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2009

### Describe in Detail

(i) Show that the arithmetic mean of (positive) regression coefficients is greater than the correlation coefficient.

(ii) What is the value of the product of geometric mean of variances and the geometric mean of regression coefficients?

### Explanation

(i) The arithmetic mean of regression coefficients is and the correlation coefficient is r.

The square of the two real numbers cannot be negative. So, the arithmetic mean of (positive) regression coeffi

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## Question number: 9

» Statistical Methods » Regression » Polynomial

Appeared in Year: 2013

### Describe in Detail

Given the two regression lines between X and Y, 2Y -X - 50 = 0,3Y-2X - 10 = 0, compute the means of X and Y and the correlation coefficient between X and Y.

### Explanation

Given that

We know that the mean value of the given series satisfies the regression line that is

The means of X and Y is calculate by multiply equation (1) by 2 to subtract equation (2), we get

The correlation coefficient is def

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## Question number: 10

» Statistical Methods » Standard Errors and Large Sample Tests

Appeared in Year: 2013

### Describe in Detail

The proportion of defective telephone instruments from the All-India basis was observed to be at 0.01. A new manufacturer of telephone instruments wants to estimate the proportion of defectives in his production lot. How many telephones should be sampled in order to estimate the fraction defective within 0.01 with 90 % confidence?

### Explanation

Let the proportion of defective telephone instruments from the All-India basis was observed to be at 0.01. The number of telephones should be sampled where the estimate fraction defective is p-p _{0} =0.01 and the true value of proportion of defective is 0.01. so, the test statistic for 90 % confidence is

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