Statistical Methods (ISS 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

f(x,y)={x+y;0<x<1,0<y<10;otherwise

Obtain correlation coefficient between X and Y

Explanation

First find the marginal distribution of X

g(x)=01f(x,y)dy

=01(x+y)dy

=[xy+y22]01

=x+12… (374 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

H0:M1=M2VsH1:M1M2

Fir this first find the difference of median

d0=M1… (210 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

β2>1

By definition of Kurtosis

β2=μ4μ22>1

μ4>μ22

Let x 1, x 2, …, x n are n observations in a set have frequency f 1,… (135 more words) …

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… (33 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

x=w1x1+w2x2++wnxnw1… (92 more words) …

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

H0:μ1=μ2againstH1:μ1μ2

at 5 % level of significance. It is given that x=2,sx2=16,y=8andsy2=15 .

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… (201 more words) …

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