ISS (Statistical Services) Statistics Paper I (Old Subjective Pattern): Questions 113 - 115 of 165

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Question number: 113

» Statistical Methods » Tests of Significance » Z-Test

Appeared in Year: 2012

Essay Question▾

Describe in Detail

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.

Explanation

The given information can be written as in a table:

Year

Smoker

Non-smoker

Total

1995

125

160

285

2012

95

230

325

Total

220

390

610

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

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Question number: 114

» Probability » Standard Probability Distributions » Normal

Appeared in Year: 2014

Essay Question▾

Describe in Detail

If f x (x) be the probability density function of a N (µ, σ 2) distribution, then show that

where , and φ (x) and Φ (x) are the probability density function and distribution function of the standard normal distribution respectively.

Explanation

Given that f X (x) be the probability density function follows N (µ, σ 2).

Then

………. (1)

Let assume that =z, then differentiate

The limit is also change, the lower limit is and upper limit is

Equation (1) can be written as

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Question number: 115

» 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 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 and represent the median time of all runner put to a r

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