Statistical Methods (ISS Statistics Paper I (Old Subjective Pattern)): Questions 51 - 54 of 72

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Question number: 51

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2012

Essay Question▾

Describe in Detail

Ten short-distance runners were put to a rigorous training for two months. Times taken by them to clear 100 metres before and after the training were as follows:

Sl. no. of runner

1

2

3

4

5

6

7

8

9

10

Time (in sec)

before

training

10.6

10.9

10.1

10.5

11.0

11.2

10.7

10.2

10.9

10.6

Time (in sec)

after

training

10.1

10.7

9.9

10.0

11.1

10.9

10.6

10.3

10.5

10.8

Use Wilcoxon’s paired sample signed rank test to examine at 1 % level if the training was at all effective. (The critical value of Wilcoxon’s statistic at 1 % level of significance for n = 10 is 5)

Explanation

In Wilcoxon’s paired sample signed rank test, the null hypothesis that we are sampling two continuous symmetric populations with μ~1=μ~2 for the paired-sample case, we rank the differences of the paired observations without regard to sign and proceed as in the single-sample case

Let… (265 more words) …

Question number: 52

» Statistical Methods » Non-Parametric Test » Run

Appeared in Year: 2013

Essay Question▾

Describe in Detail

Describe the run test for randomness. For the sequence of outcomes of 14 tosses of a coin,

HTTHHHTHTTHHTH, .

test whether the outcomes are in random order. (Given the lower and upper critical values R L = 3,

R u = 12 at 0.05 significance level. )

Explanation

Suppose a sample size n contains n 1 symbols of one type and n 2 symbols of the other type. The null hypothesis is the symbols occur in random order, the alternative is the symbols occur in a set pattern. The lower and upper critical value is obtained from tables.… (99 more words) …

Question number: 53

» Statistical Methods » Correlation Coefficient » Multiple Correlation

Appeared in Year: 2015

Essay Question▾

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With 3 variables X 1, X 2 and X 3, it is given that r 13 =0.71, R 1.23 =0.78. Find r 12.3.

Explanation

We know that

r12.3=r12r13r23(1r132)(1r232)

R1.23=r122+r1322r12r13r231r232… (95 more words) …

Question number: 54

» Statistical Methods » Correlation Coefficient » Intraclass Correlation

Appeared in Year: 2012

Essay Question▾

Describe in Detail

For a set of 10 pairs of observations (x i, y j), i = 1 (1) 10, the following calculations are available

xi=61,xi2=412,yi=45,yi2=308,xiyi=295

Examine at 5 % level of significance if the two variables arc uncorrelated in the population.

Explanation

First, we calculate the sample correlation coefficient r

r=(xix)(yiy)(xix)2(yiy)2

for i = 1 to 10

r… (173 more words) …

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