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

Equation

Obtain correlation coefficient between X and Y

Explanation

First find the marginal distribution of X

Equation

Equation

Equation

Equation

find the marginal distribution of Y

Equation

Equation

Equation

Equation

The mean of X and Y is

Equation

Equation

Equation

Equation

The second moment of X and Y is

Equation

Equation

Equation

Equation

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

Equation

Fir this first find the difference of median

Equation

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

Equation

By definition of Kurtosis

Equation

Equation

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 Equation, then

Equation

Assume Equation<span class="more">… (17 more words) …</span>

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

Equation

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

Equation

Equation

Equation

Equation

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

Equation

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

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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