# Statistical Methods [ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)]: Questions 6 - 10 of 72

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## Question number: 6

» 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: 7

» 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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## Question number: 8

» Statistical Methods » Dispersion and Skewness

Appeared in Year: 2012

### Describe in Detail

Show, by proving all intermediate results, that for a set of n unsorted data, the measure of skewness based on mean, median and standard deviation, necessarily lies between -3 and + 3.

### Explanation

The formula of measure of skewness given by Karl Pearson’s is

Also, we known the relation of mean, median and mode is

Mean-Mode = 3 (Mean-Median)

So,

Using Chebyshev’s inequality, X be a random variable with mean µ and variance

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## Question number: 9

» Statistical Methods » Dispersion and Skewness

Appeared in Year: 2010

### Describe in Detail

The first three moments of a distribution about the value 1 are 2,25 and 80. Find its mean standard deviation and the moment-measure of skewness.

### Explanation

Given that a = 1,

The mean is

The standard deviation is

Measure of skewness

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## Question number: 10

» Statistical Methods » Non-Parametric Test » Sign

Appeared in Year: 2010

### Describe in Detail

Describe clearly sign test. State its asymptotic relative efficiency with respect to t-test.

### Explanation

Let x _{(1),} x _{(2), …,} x _{(n)} be the ordered sample values from a population F (X) and M be its median.

Here we test where M _{0} is the given value of the median and hence

To perform the sign test, first find the differences (X _{(i)} -M _{0}) for i = 1,2, …, n and consider their signs. Su

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