# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 7 - 12 of 72

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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 %

## 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 σ ^{2} then any k > 0,

## 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

## 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

## Question number: 11

» Statistical Methods » Correlation Ratio

Appeared in Year: 2012

### Describe in Detail

Two persons Amal and Bimal come to the club at random points of time between 6 p. m. and 7 p. m. , and each stays for 10 minutes. What is the chance that they will meet?

### Explanation

Let *x* denote the time Amal arrives at the bar and *y* denote the time Bimal arrives at the bar from 6 p. m. We will draw the lines *y* = *x* – 10 and *y* = *x* + 10 and shade the area in between these two lines to

## Question number: 12

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

Appeared in Year: 2009

### Describe in Detail

wo drugs were given to two batches of 6 students. The numbers of days to get a complete cure are given below:

Durg A | 6 | 7 | 8 | 9 | 12 | 16 |

Durg B | 10 | 11 | 13 | 14 | 15 | 17 |

Using Mann-Whitney test decide whether the median days for cure by the two drugs are equal. (Table values of U - Statistic at 0.05 level are: U _{5, 5} = 2, U _{5, 6} = 3, and U _{6, 6} = 5. )

### Explanation

Let the Durg A consider the population X and Durg B consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Mann-Whitney test, first consider the combined ordered sequence of the sample values is

Sample: