Statistical Methods (ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern)): Questions 46 - 50 of 72

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Question number: 46

» Statistical Methods » Bivariate Distributions » Bivariate Normal Distribution

Appeared in Year: 2009

Essay Question▾

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Given the joint density of (X 1, X 2),

Find the marginal densities of X 1 and X 2. Also find E [X 1].


The joint density is written as

The marginal distribution of X 1

The marginal distribution of X 2 is

The first integral is

So, the marginal distribution of X 2 is

The mean of X 1 is

when we solve this, we get

… (-8 more words) …

Question number: 47

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2011

Essay Question▾

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Apply the Wilcoxon two-sample test to the following data on the first breakdown times of two brands of computers:

Brand A 98, 102, 47, 85, 99, 140, 130

Brand B 95, 125, 160, 155, 148.

Use 1·96 as the critical point for the appropriate test.


Let n 1 be the number of breakdown times in the Brand A with median time m 1, and n 2 the number of breakdown times in the Brand B with median time m 2. Then the hypothesis is that the median times of the two brands are equal against the alternative that they are unequal.

For this first arrange the observations of the combined samples (n 1 +n

… (112 more words) …

Question number: 48

» Statistical Methods » Non-Parametric Test » Mann-Whitney

Appeared in Year: 2015

Essay Question▾

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Consider the two samples as follows:

Sample I = 6, 7, 8, 10, 12, 14, 16, 23

Sample II: 9, 11, 13, 15, 17, 18, 19, 20, 24

Test whether the examples have come from the same population by Wilcoxon-Mann-Whitney test at 10 % level of significance. [You can use normal approximation]


Let the sample I consider the population X and sample II consider the population Y. The hypothesis whether two sample comes from same identical population. We test the following null and alternative hypothesis is

In Wilcoxon-Mann-Whitney test, first consider the combined ordered sequence of the sample values is

Sample: 6 7 8 9 10 11 12 13 14…

… (99 more words) …

Question number: 49

» Statistical Methods » Regression » Linear

Appeared in Year: 2015

Essay Question▾

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For 20 pairs of heights of father (X) and son (Y) measured in cm, the following data are obtained:

Test whether the cut on the X-axis can be assumed to be zero, at 5 % level of significance.


In the regression model, the cut on the X-axis can be assumed to be zero means the intercept zero. The test of the hypothesis is

Can be tested by the statistic is

where is the standard error of an estimator b 0.


Then, putting the value in above equation

The statistic is

Tabulated value of t 0.05, 18 =2.101, which is g…

… (5 more words) …

Question number: 50

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2012

Essay Question▾

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125out of 285 college-going male students in 1995 from a city were found to be smokers. Another sample of 325 such students from the same city in 2012 included 95 smokers. Examine at 5 % level of significance if smoking habit among college-going students is on the decrease in this city.


The given information can be written as in a table:

















Here, the null hypothesis is that the proportion of smoker in this two year is same and the alternative is there is decrease in the smoker in 2012. Le…

… (67 more words) …

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