# Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 55 - 60 of 72

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## Question number: 55

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Let (X, Y) be jointly distributed with density function

Obtain correlation coefficient between X and Y

### Explanation

First find the marginal distribution of X

find the marginal distribution of Y

The mean of X and Y is

The second moment of X and Y is

The variance of X and Y… (24 more words) …

## Question number: 56

» Statistical Methods » Non-Parametric Test » Sign

Appeared in Year: 2011

Essay Question▾

### Describe in Detail

Let the temperature before and after administration of aspirin be

 Patient Before After 1 100.0 98.1 2 102.1 97.2 3 100.6 98.6 4 100.1 99.1 5 101.5 97.6 6 102 98.6 7 99.9 98.2 8 102.7 98.1 9 100.40 98.2 10 100.8 97.1

Test by the sign test; whether aspirin is effective in reducing temperature. What is the p-value of the calculated statistic?

### Explanation

Let M 1 and M 2 is the median temperature of the patients. The hypothesis for test is

Fir this first find the difference of median

Also find the difference of temperature of before and after

d i 2.1 4.9 2.0 1.0 3.9 3.4 1.7 4.6 2.4 3.7… (131 more words) …

## Question number: 57

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

Show that for discrete distribution β 2 > 1

### Explanation

We have to prove that

By definition of Kurtosis

Let x 1, x 2, …, x n are n observations in a set have frequency f 1, f 2, …, f n and the mean of observation is , then

Assume

## Question number: 58

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2010

Essay Question▾

### Describe in Detail

How large a sample must be taken in order that the probability will be at least 0.95 that X n will be within 0.5 of µ (µ is unknown and σ = l).

### Explanation

Here, you would know the standard deviation of a population but not know the mean of that population. So, you want to estimate the mean μ to within a given margin of error in a given confidence interval. The required sample size is

Margin of error E = 0.5,

1-α=0.95… (11 more words) …

## Question number: 59

» Statistical Methods » Measures of Location

Appeared in Year: 2013

Essay Question▾

### Describe in Detail

Find the weighted arithmetic mean of the first ‘n’ natural numbers, the weights being the corresponding numbers.

### Explanation

If x 1, x 2, …, x n are the values having weights w 1, w 2, …, w n respectively, the weight mean is

Here X is first ‘n’ natural numbers that is 1, 2, 3, …, n

## Question number: 60

» Statistical Methods » Tests of Significance » T-Test

Appeared in Year: 2015

Essay Question▾

### Describe in Detail

Let X 1, X 2, …, X 12 be a random sample from a normal N (µ 1, σ 12) and Y 1, Y 2, …Y 10 be another random sample from normal N (µ 2, σ 22), independently to each other. Carry out an appropriate test for testing

at 5 % level of significance. It is given that .

### Explanation

Let X 1, X 2, …, X 12 be a random sample from a normal N (µ 1, σ 12) and Y 1, Y 2, …Y 10 be another random sample from normal N (µ 2, σ 22), independently to… (87 more words) …

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