# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 18 - 23 of 72

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## Question number: 18

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2015

### Describe in Detail

Let (X, Y) be distributed as bivariate normal BVN (3, 1, 16, 25, 3/5). Calculate P (4 < Y < 11.84|X=7)

### Explanation

We had known that the conditional distribution of Y given X has mean and variance .

Using conditional mean and variance

## Question number: 19

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2009

### Describe in Detail

A manufacturer of alkaline batteries expects that only 5 % of his products are defective. A random sample of 300 batteries contained 10 defectives. Can we conclude the proportion of defectives in the entire lot is less than 0.5 at 5 % level of significance?

### Explanation

A random sample of 300 batteries contained 10 defectives. A manufacturer of alkaline batteries expects that only 5 % of his products are defective that is testing of hypothesis is

H _{0}: P = 0.05 against H _{1}: P < 0.05

Here n = 300, numbers of defectives

## Question number: 20

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2010

### Describe in Detail

You are working as a purchase manager for a company. The following information has been supplied to you by two manufacturers of electric bulbs.

Company A | Company B | |

Mean life | 1300 | 1288 |

Standard deviation | 82 | 93 |

Sample size | 100 | 100 |

Which brand of bulbs are you going to purchase if you desire to take a risk of 5%?

### Explanation

Here the sample size is n = 100

The standard deviation and mean of two samples is different. The null hypothesis is the mean life of bulb of company A is equal to the mean life of bulb of company B and alternative its differ.

The test statistic is

## Question number: 21

» Statistical Methods » Measures of Location

Appeared in Year: 2011

### Describe in Detail

Let Z be a random variable with p. d. f. f (z). Let z _{α} be its upper α ^{th} quantile. Show that if X is

a random variable with p. d. f. then σz _{α} +µ is the upper α ^{th} quantile of X.

### Explanation

Let Z be a random variable with p. d. f. f (z). Given that the quantile of z is defined as

X is a random variable with p. d. f. , then quantile is

Assume

Then the limit is

Lower limit is - and upper

## Question number: 22

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2012

### Describe in Detail

Name two non-parametric tests for comparing locations of two correlated populations.

### Explanation

The Wald-Wolfowitz runs test and Mann-Whitney U-test comparing locations of two correlated populations. Let the sample 1 consider the population X and sample 2 consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

## Question number: 23

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

Appeared in Year: 2013

### Describe in Detail

The values of two random samples are arranged below in an increasing order with X denoting the value of sample I and Y denoting the value of sample 2:

XXXYXYYYYXXYXXXYXXYYY

Use Wald-Wolfowitz run test to test whether the two samples may be regarded as coming from a common population.

### Explanation

Wald-Wolfowitz run test uses the data of two random samples, sample 1 is X variables of size n = 11 and sample 2 is Y variables of size m = 10 from two population F _{X} (x) and F _{Y} (y) respectively.

The hypothesis under the test is that the