Statistical Methods (ISS 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

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

f(x1,x2)={18(x12x22)ex1;0<x1<, x2 <x10;otherwise

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


The joint density is written as

f(x1,x2)={18(x12x22)ex1;0<x1<,x1<x2<x10;… (395 more words) …

Question number: 47

» Statistical Methods » Non-Parametric Test » Wilcoxon

Appeared in Year: 2011

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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… (273 more words) …

Question number: 48

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

Appeared in Year: 2015

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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

H0:FX(x)=FY(x)Vs… (282 more words) …

Question number: 49

» Statistical Methods » Regression » Linear

Appeared in Year: 2015

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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

t=… (199 more words) …

Question number: 50

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2012

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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… (199 more words) …

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